references to publications of - university of south carolinapeople.math.sc.edu/laszlo/cita.pdf ·...

References to publications of

L. A. Szekely

November 24, 2010

1./ L. A. Szekely, Remarks on the chromatic number of geometricgraphs, in: Graphs and Other Topics (ed. M. Fiedler), Teubner-Texte zur Mathematik, Band 59, Leipzig, l983, 312–315.

References

1. Fernando Mario de Oliveira Filho, New Bounds for Geometric Packingand Coloring via Harmonic Analysis and Optimization, Ph.D. Thesis,Centrum Wiskunde & Informatica in Amsterdam, 2009.

2. FERNANDO MARIO DE OLIVEIRA FILHO AND FRANK VAL-LENTIN, A QUANTITATIVE VERSION OF STEINHAUS THEO-REM FOR COMPACT, CONNECTED, RANK-ONE SYMMETRICSPACES, arXiv:1005.0471v1 [math.CO] 4 May 2010

3. Hart, Derrick, Explorations of geometric combinatorics in vector spacesover finite fields, Ph.D., UNIVERSITY OF MISSOURI - COLUMBIA,2008, 70 pages

4. Hart D, Iosevich A, Ubiquity of simplices in subsets of vector spacesover finite fields, ANALYSIS MATHEMATICA Volume: 34 Issue: 1Pages: 29-38 Published: JAN 2008

5. M. S. Payne, D. Coulson, A dense distance 1 excluding set in R3,Austr. Math. Soc. Gaz. 34 (2) (2007), 97–102.

6. P. Brass, W. Moser, J. Pach, Research Problems in Discrete Geometry,2005, 499 pages.

7. P. Erdos, Some combinatorial, geometric, and set theoretic problemsin measure theory, in: Measure Theory, Oberwolfach, 1983, eds. D.Kolzow, D. Maharam-Stone, Springer Lecture Notes in MathematicsVol. 1089, Springer-Verlag, 1984, 321–327.

8. K. J. Falconer, The realization of small distances in plane sets of pos-itive measure, Bull. London Math. Soc. 18(1986), 471–474.

9. K. J. Falconer, J. M. Marstrand, Plane sets of positive density at infin-ity contain all large distances, Bull. London Math. Soc. 18(1986),475–477.

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10. J. Bourgain, A Szemeredi-type theorem for sets of positive density inRn, Israel J. Math 54(1986), 307–316. (This paper actually did notgive a citation to my work, although clearly ought to have done.)

11. H. Furstenberg, Y. Katznelson, B. Weiss, Ergodic theory and con-figurations in sets of positive density, in: Mathematics of RamseyTheory, J. Nesetril, V. Rodl, eds., Algorithms and Combinatorics 5,Springer Verlag, 1990, 184–198.

12. H. T. Croft, K. J. Falconer, R. K. Guy, Unsolved Problems in Ge-ometry, Problem Books in Mathematics, Springer-Verlag, 1991.

2./ L. A. Szekely, Measurable chromatic number of geometric graphsand sets without some distances in Euclidean space, Combina-torica 4(1984), 213–218.

References

1. M. S. Payne, Unit distance graphs with ambiguous chromatic number,Electronic J. Combinatorics 16 (2009) pp. 7.

2. F. M. de Oliveira Filho, F. Vallentin, Fourier analysis, linear program-ming and densities of distance avoiding sets in Rn



5. L. Lovasz and K. Vesztergombi, Geometric representations of graphs,in: Paul Erdos and his Mathematics II, Bolyai Studies 11, Springer-Verlag, 2002, 471–498.

6. P. Erdos, Some combinatorial and metric problems in geometry, in:Intuitive Geometry, Siofok, 1985, Coll. Math. Soc. J. Bolyai48(1987), 167–177.


8. L. Babai, P. Frankl, Linear Algebra Methods in Combinatorics,Part 1, Preliminary Version, July 1988, Department of Computer Sci-ence, The University of Chicago. (Also Preliminary Version 2, Septem-ber 1992).

9. R. B. Eggleton, 3 unsolved problems in graph theory, Ars Combina-toria 23A(1987), 105–121.

10. A. Raigorodskii, Borsuk’s problem and the chromatic number of cer-tain metric spaces, Russ. Math. Surv. 56 (1) (2001) 103–109.

11. Raigorodskii, A.M. Borsuk’s problem and the chromatic numbers ofmetric spaces (2007) Electronic Notes in Discrete Mathematics, 28,pp. 273-280.

3./ L. A. Szekely, On the number of homogeneous subgraphs of agraph, Combinatorica 4(1984), 363–372.

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References

1. David Conlon, On the Ramsey Multiplicity of Complete Graphs, arXiv:0711.4999v1[math.CO] 30 Nov 2007

2. J. Cutler, B. Montagh,Unavoidable subgraphs of colored graphs, DIS-CRETE MATHEMATICS Volume: 308 Issue: 19 Pages: 4396-4413Published: OCT 6 2008

3. A. Thomason, The simplest case of Ramsey’s theorem, in: Paul Erdosand his Mathematics II, Bolyai Studies 11, Springer-Verlag, 2002, 667–695.

4. A. Thomason, Random graphs, strongly regular graphs and pseudo-random graphs, in: Surveys in Combinatorics, LMS Lecture Notes123, C.U.P., Cambridge, 1987, 173–195.

4./ L. A. Szekely, On two concepts of discrepancy in a class of com-binatorial games, in: Finite and Infinite Sets, Coll. Math. Soc.Janos Bolyai 37(1985), 679–683.

References

1. AS Fraenkel, Combinatorial games: selected bibliography with a suc-cinct gourmet introduction, the electronic journal of combinatorics(2009), #DS2

2. J. Beck, Inevitable randomness in discrete mathematics, UniversityLecture Notes Series 49, AMS, 2009.

3. Andras Csernenszky, The PickerChooser diameter game, TheoreticalComputer Science Volume 411, Issues 40-42, 6 September 2010, Pages3757-3762

4. J. Beck, Surplus of Graphs and the Lovsz Local Lemma, BuildingBridges Bolyai Society Mathematical Studies, 2008, Volume 19, 47-102, DOI: 10.1007/978-3-540-85221-6 2

5. Balogh J, Martin R, Pluhar A, The Diameter Game, RANDOM STRUC-TURES & ALGORITHMS 35 (2009) 3 369–389.

6. Feldheim ON, Krivelevich M, Winning Fast in Sparse Graph Construc-tion Games, COMBINATORICS PROBABILITY & COMPUTINGVolume: 17 Issue: 6 Pages: 781-791 Published: NOV 2008

7. J. Beck, Combinatorial Games: Tic-Tac-Toe Theory, Cambridge Uni-versity Press, 2008, 746 pages.

8. Alon N, Krivelevich M, Spencer J, et al. Discrepancy games ELEC-TRONIC JOURNAL OF COMBINATORICS 12 (1): Art. No. R51SEP 29 2005

9. Frieze A, Krivelevich M, Pikhurko O, et al. The game of JumbleGCOMBINATORICS PROBABILITY & COMPUTING 14 (5-6): 783-793 SEP-NOV 2005

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10. J. Beck, Deterministic graph games and a probabilistic intuition, Com-binatorics, Probability and Computing 3(1994), 13–26.

11. J. Beck, Achievement games and the probabilistic method, Combi-natorics, Paul Erdos is Eighty (Volume 1), Keszthely, Hungary,1993, eds. D. Miklos, V. T. Sos, T. Szonyi, Bolyai Society Mathemat-ical Studies 1, 51–78.

12. J. Beck, Games, randomness, and algorithms, in: The Mathematicsof Paul Erdos vol. I, eds. R. L. Graham and J. Nesetril, Algorithmsand Combinatorics 13, Springer-Verlag, 1997, 280–310.

5./ L. A. Szekely, A note on common origin of cubic binomial identi-ties, a generalisation of Suranyi’s proof on Le Jen Shoo’s formula,J. Comb. Theory Ser. A 40(1985), 171–174.

References

1. Kadell KWJ Telescoping partial fractions decompositions, the little q-Jacobi functions of complex order, and the nonterminating q-Saalschutzsum RAMANUJAN JOURNAL 13 (1-3): 449-469 JUN 2007

2. Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, page2927.

3. Eric W. Weisstein. ”Szekely Identity.” From MathWorld–A WolframWeb Resource.http://mathworld.wolfram.com/SzekelyIdentity.html

4. Jiang Zeng, Pfaff-Schaalschutz revisited, J. Comb. Theory Ser. A51(1989), 141–143.

5. V. Strehl, Binomial identities—combinatorial and algorithmic aspects,Disc. Math. 136(1994), 309–346.

6. R. A. Proctor, D. C. Wilson, Interpretation of a basic hypergeomet-ric identity with Lie characters and Young tableaux, Disc. Math.137(1995), 297–302.

6./ L. A. Szekely, Holiday numbers: sequences resembling the Stir-ling numbers of second kind, Acta Sci. Math. (Szeged) 48(1985),459–467.

References

1. Wang, Yi; Yeh, Yeong-Nan Polynomials with real zeros and Po’lyafrequency sequences. J. Combin. Theory Ser. A 109 (2005), no. 1,63–74

2. Klazar M, Luca F On some arithmetic properties of polynomial expres-sions involving Stirling numbers of the second kind ACTA ARITH 107(4): 357-372 2003

3. H. K. Hwang, Asymptotics of Poisson approximation to random dis-crete distributions: An analytic approach Adv. Appl. Probability,31 (2) 1999, 448–491

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7./ A. Bogmer and L. A. Szekely, Asymptotic formula for the numberof solutions of a diophantic system, Annales Univ. Sci. Bud.Eotvos 28(1985), 203–215.

References

1. I. Joo, On the number of partitions of N into terms of 1, 2, ..., n, re-peating a term at most n times, Annales Univ. Sci. Bud. Eotvos28(1985), 217–227.

2. G. O. H. Katona, Ramanujan’s work in the theory of partitions, J.Indian Inst. Sci. (1987), 33–38.

8./ L. A. Szekely and N. C. Wormald, Generating functions for theFrobenius problem with 2 or 3 generators, Math. Chronicle15(1986), 49–57.

References

1. David Einstein, Daniel Lichtblau, Adam Strzebonski, Stan WagonFROBENIUS NUMBERS BY LATTICE POINT ENUMERATIONINTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUM-BER THEORY 7 (2007), #A15

2. Aicardi F, Fel LG, Gaps in nonsymmetric numerical semigroups, IS-RAEL JOURNAL OF MATHEMATICS 175(1)(2010) 85–112

3. Holroyd AE, Partition identities and the coin exchange problem JOUR-NAL OF COMBINATORIAL THEORY SERIES A Volume: 115 Is-sue: 6 Pages: 1096-1101 Published: AUG 2008

4. K Woods, Rational generating functions and lattice point sets, Ph. D.Thesis, University of Michigan, 2004

5. Leonid G. Fel, Frobenius problem for semigroups S(d1, d2, d3), 2006,Functional Analysis and Other Mathematics Volume 1, Number 2,119-157, DOI: 10.1007/s11853-007-0009-5

6. LG Fel, Analytic Representations in the 3-dim Frobenius Problemarxiv.orgLG Fel - Arxiv preprint math/0507370, 2005 - arxiv.org

7. Denham G Short generating functions for some semigroup algebrasELECTRON J COMB 10 (1): Art. No. R36 2003

8. A. Barvinok, J. E. Pommersheim, An algorithmic theory of latticepoints in polyhedra, New Perspectives in Geometric CombinatoricsMSRI Publications 38, 1999, 91–147.

9. Barvinok, A; Woods, K, Short rational generating functions for latticepoint problems, JOURNAL OF THE AMERICAN MATHEMATI-CAL SOCIETY; 2003; v.16, no.4, p.957-979.

9./ L. A. Szekely, The analytic behaviour of the holiday numbers,Acta Sci. Math. (Szeged) 51(1987), 365–369.

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References

1. Wang, Yi; Yeh, Yeong-Nan Polynomials with real zeros and Po’lyafrequency sequences. J. Combin. Theory Ser. A 109 (2005), no. 1,63–74

2. Klazar, Martin; Luca, Florian On some arithmetic properties of poly-nomial expressions involving Stirling numbers of the second kind. ActaArith. 107 (2003), no. 4, 357–372.

3. H. K. Hwang, Asymptotics of Poisson approximation to random dis-crete distributions: An analytic approach Adv. Appl. Probability,31 (2) 1999, 448–49

10./ P. Erdos, I. Joo and L. A. Szekely, Remarks on infinite series,Studia Sci. Math. Hung. 22(1987) (1-4), 395–400.

References

1. M. Szegedy, G. Tardos, On the decomposition of infinite series intomonotone decreasing parts, Studia Sci. Math. Hung. 23(1988),81–84.

2. M. Horvath, Answer to a problem of Joo, Studia Sci. Math. Hung.23(1988), 245–250.

11./ L. A. Szekely, Inclusion-exclusion formulae without higher terms,Ars Comb. 23B(1987), 7–20.

References

1. D. A. Grable, Hypergraphs and sharpened sieve inequalities, DiscreteMath. 132 (1994)(1-3), 75–82.

2. D. de Caen, A lower bound on the probability of a union, DiscreteMath. 169(1997), no. 1-3, 217–220.

12./ L. A. Szekely and N. C. Wormald, Bounds on the measurablechromatic number of Rn, Discrete Math. 75(1989), 343–372.(Also published as: Bounds on the measurable chromatic numberof Rn, in: Graph Theory and Combinatorics 1988, Proceedingsof the Cambridge Combinatorial Conference in Honour of PaulErdos, ed. B. Bollobas, Annals of Discrete Mathematics 43,North-Holland, 1989, 343–372.)

References


2. C. Bachoc, G. Nebe, F. M. de Oliveira Filho, F. Vallentin, Lowerbounds for measurable chromatic numbers, GEOMETRIC AND FUNC-TIONAL ANALYSIS 19 (2009) Issue: 3 Pages: 645-661.

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4. page 254, CRC Handbook of Discrete and Computational Geometry,(E.Goodman, J. O’Rourke, eds.), CRC Press, 1997.


6. R. Radoicic, G. Toth, A note on the chromatic number of R3, Discreteand Computational Geometry—The Goodman–Pollack Festschrift(Algebra and Combinatorics 25), Springer-Verlag, 2003.

7. O. Nechustan, On the space chromatic number, Discrete Math. 256(1-2) (2002), 499–507

8. T. R. Jensen and B. Toft, Graph Coloring Problems, Wiley-Interscience,1995.

9. V. Klee, S. Wagon, Old and New Unsolved Problems in Plane Ge-ometry and Number Theory, MAA Dolciani Expositions No. 11,1991, Providence, RI.


11. L. Babai, P. Frankl, Linear Algebra Methods in Combinatorics,Part 1, Preliminary Version, July 1988, Department of Computer Sci-ence, The University of Chicago. (Also Preliminary Version 2, Septem-ber 1992).

12. K. Cantwell, Edge-Ramsey theory, Discrete Comput. Geom. 15(1996)(3), 341–352.

13. K. Cantwell, Finite Euclidean Ramsey theory, J. Combin. Theory A73(1996), 273–285.

14. D. Coulson, An 18-colouring of 3-space omitting distance one, DiscreteMath. 170(1997), 241–247.

13./ P. L. Erdos and L. A. Szekely, Applications of antilexicographicorder I: An enumerative theory of trees, Adv. Appl. Math.10(1989), 488–496

References

1. Jacob Post, COMBINATORICS OF ARC DIAGRAMS, FERRERSFILLINGS, YOUNG TABLEAUX AND LATTICE PATHS, Master’sthesis in Computing Science, 2001, Simon Fraser University.

2. B. Vance, Counting ordered trees by permuting their parts, Amer.Math. Monthly 2006 113 (4): 329-335

3. Donald E. Knuth, The Art of Computer Programming, Vol. 4, Sec-tions 7.2.1.5: Generating All Partitions, Exercise 10, Addison–Wesley,2005.

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4. C. Semple and M. Steel, Phylogenetics, Oxford Lecture Series in Math-ematics and its Applications 24, Oxford University Press, 2003

5. Akos Toroczkai, On the topological classification of binary trees usingthe Horton-Strahler index, Phys. Rev. E 6501 (1): 6130-+ Part 2JAN 2002.

6. P. Hilton, J. Pedersen, Two recurrence relations for Stirling factors,Bull. Belg. Math. Soc.-Sim. 6 (4) (1999), 615–623.

7. P. W. Diaconis, and S. P. Holmes, Matchings and phylogenetic trees,Proc. Natl. Acad. Sci. USA 95(25) (1998), 14600-14602.

8. W. Y. Chen, A general bijective algorithm for trees, Proc. Natl.Acad. Sci. USA 87(1990), 9635–9639.

9. W. Y. C. Chen, On the combinatorics of plethysm, Ph. D. Thesis, M.I. T., Cambridge, Ma., 1991.

10. M. A. Steel, The complexity of reconstructing trees from qualitativecharacters and subtrees, J. Classification 9(1992), 91–116.

11. P. L. Erdos, A new bijection on rooted forests, Discrete Math. 111(1993), 179–188.

12. R. P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge Uni-versity Press, 1999.

13. M. A. Steel, Decompositions of leaf-coloured binary trees, Adv. Appl.Math. 14(1993), 1–24.

14. R. Ehrenborg, M. Mendez, Schroder parenthesizations and chordates,J. Comb. Theory Ser A 67(1994), 127–139.

15. M. Hendy, P. Hilton, J. Pedersen, Stirling factors and phylogenetictrees, Journees Mathematiques & Informatique 5(1994), 110–122.

16. T. Bier, Remarks on the algebra of calculus, manuscript.

14./ T. D. Porter and L. A. Szekely, Generating functions for a prob-lem of Riordan, J. Comb. Math. Comb. Comput. 6(1989),195–198.

References

1. T. D. Porter, Some results in combinatorial analysis and graph theory,Ph. D. Thesis, University of New Mexico, Albuquerque, NM, 1990.

15./ M. Carter, M. Hendy, D. Penny, L. A. Szekely and N. C. Wormald,On the distribution of length of evolutionary trees, SIAM J. Dis-crete Math. 3(1990), 38–47.

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References

1. M. Steel, The Penny Ante: Mathematical biology or biological math-ematics? New Zealand Science Review Vol 66 (1) 2009 12–13.

2. Quantifying the potential utility of phylogenetic characters Author(s):Cotton JA, Wilkinson M Source: TAXON Volume: 57 Issue: 1 Pages:131-136 Published: FEB 2008

3. D. Cieslik, Shortest Connectivity, An Introduction with Applicationsin Phylogeny, Springer, 2005.

4. Semple C, Steel M Unicyclic networks: Compatibility and enumerationIEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGYAND BIOINFORMATIOCS 3 (1): 84-91 JAN-MAR 2006

5. D Bryant, The Splits in the Neighborhood of a Tree, Annals of Com-binatorics 8 (2004) 1-11

6. T Dezulian, M Steel, Phylogenetic closure operations and homoplasy-free evolution, Proceedings of the 2004 International Federation ofClassification Societies, Springer- Verlag (in press)

7. Arias JS, Miranda-Esquivel DR Profile Parsimony (PP): an analysisunder Implied Weights (IW) CLADISTICS 20 (1): 56-63 FEB 2004

8. J. Felsenstein, Inferring Phylogenies, Sinauer Associates, 2004.


10. Dorit S. Hochbaum, Anu Pathria, Path Costs in Evolutionary TreeReconstruction (1997) Journal of Computational Biology

11. Dan Faith, Syst. Biol.12. K. Hewitt, Blocks as a tool for learning: Historical and contemporary

perspectives, Young Children 56 (1) (2001).

13. M. A. Steel, Distribution on bicoloured binary trees arising from theprinciple of parsimony, Discrete Appl. Math. 41(1993), 245–261.

14. C. Semple, M. Steel, Tree reconstruction from multistate characters,Adv. Appl. Math. 28 (2002), 169–184.

15. M. A. Steel, Distributions on bicoloured evolutionary trees, Ph. D.Thesis, Massey University, Palmerston North, New Zealand, 1989.

16. M. A. Steel, The complexity of reconstructing trees from qualitativecharacters and subtrees, J. Classification 9(1992), 91–116.


18. M. A. Steel, M. D. Hendy, D. Penny, The significance of the length ofthe shortest tree, J. Classification 9(1992), 71–90.

19. D. Penny, M. D. Hendy, M. A. Steel, Testing the theory of descent, in:Phylogenetic analysis of DNA sequences, eds. M. M. Miyamoto,Oxford Univversity Press, Oxford, 1991, 155–183.

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20. J. B. Slowinski, Unordered versus ordered characters, Syst. Biol.42(1993) (2), 155–165.

21. P. A. Goloboff, Homoplasy and the choice among cladograms, Cladis-tics 7 (1991) (3), 215–232.

22. W. P. Maddison, M. Slatkin, Null models for the number of evolution-ary steps in a character on a phylogenetic tree, Evolution 45 (1991)(5) 1184-1197.

23. J. W. Moon, M. A. Steel, A limiting theorem for parsimoniously bi-coloured trees, Appl. Math. Letters 6(4)(1993), 5–8.

24. P. L. Erdos, A new bijection on rooted forests, Discrete Math. 111(1993),179–188.

25. H. H. Bock Probabilistic models in cluster analysis, Comput. Stat.Data An. 23 (1996)(1) 5–28.

26. A. M. Hamel, M. A. Steel, The length of a leaf colouration on a randombinary tree, SIAM Discrete Math. 10 (1997), no. 3, 359–372.

27. M. A. Steel, L. Goldstein, and M. S. Waterman, A central limit theo-rem for parsimony length of trees, Adv. Appl. Probability, 28(1996),1051–1071.

28. D. S. Hochbaum, A. Pathria, Path costs in evolutionary tree recon-struction, J. Comput. Biol. 4(1997) (2), 163–175.

29. E. Matisoo-Smith, R. M. Roberts, G. J. Irwin, et al., Patterns ofprehistoric human mobility in Polynesia indicated by mtDNA fromthe Pacific rat, Proc. Natl. Acad. Sci. USA 95 (25), 15145–15150.

30. L. J. Collins, V. Moulton, D. Penny, Use of RNA secondary structurefor studying the evolution of RNase P and RNase MRP, J. Mol. Evol.51 (2000), 194–204.

16./ T. D. Porter and L. A. Szekely, On a matrix discrepancy prob-lem, Congr. Num. 73(1990), 239–248.

References

1. Baogang Xua, Juan Yana, and Xingxing Yu, A note on balanced bi-partitions, Discrete Mathematics Volume 310, Issue 20, 28 October2010, Pages 2613-2617

2. Jie Maa and Xingxing Yu, Bounds for pairs in partitions of graphs,Discrete Mathematics Volume 310, Issues 15-16, 28 August 2010, Pages2069-2081

3. Rui Li, Baogang Xu, Biased Judicious Partition of Graphs

4. Baogang Xu, Juan Yan, Xingxing Yu, Balanced judicious bipartitionsof graphs, Journal of Graph Theory Volume 63, Issue 3, pages 210225,March 2010


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6. Bollobas, B.; Scott, A. D. Problems and results on judicious parti-tions. Random structures and algorithms (Poznan, 2001). RandomStructures Algorithms 21 (2002), no. 3-4, 414–430.

7. T. D. Porter, Graph partitions, J. Comb. Math. Comb. Comput.15(1994), 111–118.

8. T. D. Porter, Minimal partitions of a graph, Ars Combinatoria 53(1999), 181–186.

9. T. D. Porter, and Bing Yang, Graph partitions II, J. Comb. Math.Comb. Comput. 37(2001), 149–158.

17./ A. A. Kooshes, B. M. E. Moret and L. A. Szekely, Improvedbounds on the prison yard problem, Congr. Num. 76(1990),145–149.

References

1. Z. Furedi, D. Kleitman, The prison yard problem, Combinatorica14(1994), 287–300.

2. A. A. Kooshesh, Structuring techniques for path and visibility prob-lems, Ph. D. Thesis, University of New Mexico, Albuquerque, NM,1992.

18./ L. H. Clark, J. I. McCanna, R. C. Entringer and L. A. Szekely,Extremal problems for local properties of graphs, AustralasianJ. Comb. 4(1991), 25–31.

References

1. N Alon, A Shapira, On an Extremal Hypergraph Problem of Brown,Erdos and Sos Combinatorica, 26 (6) (2006) 627–645.

2. Mieczyslaw Borowiecki, Elzbieta Sidorowicz, Some extremal problemsof graphs with local constraints, Discrete Mathematics 251 (2002),19–32.

3. Borowiecki, Mieczyslaw; Mihok, Peter On graphs with a local heredi-tary property. Graph theory (Kazimierz Dolny, 1997). Discrete Math.236 (2001), no. 1-3, 53–58.

4. J. I. McCanna, The classification of self-dual graphs and other resultsin graph theory, Ph. D. Thesis, University of New Mexico, Albu-querque, NM, 1990.

5. Akos Seress, Polygonal Graphs, Horizons of Combinatorics Bolyai So-ciety Mathematical Studies, 2008, Volume 17, 179-188, DOI: 10.1007/978-3-540-77200-2 9

6. A. Seress, T. Szabo, Dense graphs with cycle neighbourhoods, J.Comb. Theory Ser. B 63(1995), 281–293.

7. T. Szabo, Extremal problems for graphs and hypergraphs, Ph. D.Thesis, Ohio State University, Columbus, 1996.

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19./ K. A. Johnson, R. Grassl, J. I. McCanna and L. A. Szekely,Pascalian rectangles modulo m, Quaest. Math. 14(1991), 383–400.

References

1. Graham N., , Harary F., , Livingston M., , Stout Q. F., (1993/02).”Sub-cube Fault-Tolerance in Hypercubes.” Information and Computation102(2): 280-314.

2. Peyman Nayeri, Charles J. Colbourn and Goran Konjevod, Random-ized Postoptimization of Covering Arrays, Lecture Notes in ComputerScience, 2009, Volume 5874/2009, 408-419, DOI: 10.1007/978-3-642-10217-2 40

3. J. I. McCanna, The classification of self-dual graphs and other resultsin graph theory, Ph. D. Thesis, University of New Mexico, Albu-querque, NM, 1990.

20./ L. A. Szekely, L. H. Clark and R. C. Entringer, An inequalityfor degree sequences, Discrete Math. 103(1992), 293–300.

References

1. Antal Ivanyi, Reconstruction of complete interval tournaments. II.Acta Univ. Sapientiae, Mathematica, 2, 1 (2010) 4771.

2. SN Qiao, On The Zagreb Index Of Quasi-Tree Graphs, Applied Math-ematics E-Notes, 10(2010), 147-150. Available free at mirror sites ofhttp://www.math.nthu.edu.tw

3. S Zhang, W Wang, TCE Cheng, Bicyclic graphs with the first threesmallest and largest values of the first general Zagreb index, Com-munications in Mathematical and in Computer Chemistry / MATCH2006, vol. 56, (3), pp. 579–592

4. Guo YL, Du YJ, Wang Y, BIPARTITE GRAPHS WITH EXTREMEVALUES OF THE FIRST GENERAL ZAGREB INDEX, MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTERCHEMISTRY 63(2) (2010) 469–480.

5. Lo ASL, Triangles in Regular Graphs with Density Below One Half,COMBINATORICS PROBABILITY & COMPUTING Volume: 18Issue: 3 Pages: 435-440 Published: MAY 2009

6. : Cheng TCE, Guo YL, Zhang SG, et al., Extreme values of the sum ofsquares of degrees of bipartite graphs, DISCRETE MATHEMATICSVolume: 309 Issue: 6 Pages: 1557-1564 Published: APR 6 2009

7. Yeon Soo Yoon, Ju Kyung Kim, A relationship between bounds on thesum of squares of degrees of a graph, J. Appl. Math. & Computing21 (2006) 233–238.

8. Cioaba SM Sums of powers of the degrees of a graph DISCRETEMATHEMATICS 306 (16): 1959-1964 AUG 28 2006

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9. Yu AM, Lu M, Tian F On the spectral radius of graphs LINEARALGEBRA AND ITS APPLICATIONS 387: 41-49 AUG 1 2004

10. Zhang SG, Zhang HL Unicyclic graphs with the first three smallestand largest first general Zagreb index MATCH-COMMUNICATIONSIN MATHEMATICAL AND IN COMPUTER CHEMISTRY 55 (2):427-438 2006

11. Gutman I, Das KC The first Zagreb index 30 years after MATCH-COMMUN MATH CO (50): 83-92 FEB 2004

12. Furedi Z, Kundgen A Moments of graphs in monotone families JOUR-NAL OF GRAPH THEORY 51 (1): 37-48 JAN 2006

13. K. C. Das, Sharp bounds for the sum of the squares of the degrees ofa graph, Kragujevac J. Math.

14. K. C. Das, Maximizing the sum of the squares of the degrees of agraph, DISCRETE MATHEMATICS 285 (1-3): 57-66 AUG 6 2004

15. Y. Caro and R. Yuster, Graphs with large variance, Ars Combinato-ria 57 (2000), 151–162.

16. H. Alzer, An inequality for increasing sequences and its integral ana-logue, Discrete Math. 133(1994), 279–283.

17. D. de Caen, An upper bound on the sum of squares of degrees in agraph, Discrete Math. 185 (1998) (1-3), 245–248.

21./ P. L. Erdos, P. Frankl, D. J. Kleitman, M. E. Saks and L. A.Szekely, Sharpening the LYM inequality, Combinatorica 12(1992),287–293.

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2. Chehreghani MH, Chehreghani MH, Lucas C, et al., Efficient rulebased structural algorithms for classification of tree structured data,INTELLIGENT DATA ANALYSIS Volume: 13, 1 165-188 : 2009


4. Heuberger C, Wagner SG, Maximizing the number of independent sub-sets over trees with bounded degree JOURNAL OF GRAPH THEORYVolume: 58 Issue: 1 Pages: 49-68 Published: MAY 2008

5. Hua Wang, Sums of distances between vertices-leaves in k-ary trees,Bull. Inst. Comb. Appl.

110

6. M. Hamina, M. Peltola, Least-central subtrees, center and centroid ofa tree

7. Hua Wang, The extremal values of the Wiener index of a tree with agiven degree sequence

8. R. Kirk, Hua Wang, Largest number of subtrees of trees with a givenmaximum degree, SIAM JOURNAL ON DISCRETE MATHEMAT-ICS Volume: 22 Issue: 3 Pages: 985-995 Published: 2008

9. Teufl, E., Wagner, S. Enumeration problems for classes of self-similargraphs (2007) Journal of Combinatorial Theory. Series A, 114 (7), pp.1254-1277.

10. Yan, W., Yeh, Y. N., Enumeration of subtrees of trees, Enumeration ofsubtrees of trees THEORETICAL COMPUTER SCIENCE 369 (1-3):256-268 DEC 15 2006

11. The On-Line Encyclopedia of Integer Sequences, A092781.http://www.research.att.com/˜njas/sequences

12. Hua Wang, Subtrees of Trees, Wiener Index and Related Problems,Ph. D. Thesis, University of South Carolina, 2005.

13. C. Heuberger, H. Prodinger, On α-greedy expansions of numbers, Ad-vances in Applied Mathematics 38 (2007)(4): 505-525

14. S. Wagner, Correlation of graph-theoretical indices, SIAM JOURNALON DISCRETE MATHEMATICS 21 (1): 33-46 2007

92./ L. A. Szekely, Progress on crossing number problems, SOFSEM2005: Theory and Practice of Computer Science: 31st Confer-ence on Current Trends in Theory and Practice of ComputerScience Liptovsky Jan, Slovakia, January 22-28, 2005. Editors:P. Vojtas, M. Bielikova, B. Charron-Bost, et al. Lecture Notesin Computer Science Vol. 3381, 2005, Springer-Verlag, 53–61.

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3. Pinchasi, R. Linear algebra approach to geometric graphs (2007) Jour-nal of Combinatorial Theory. Series A, 114 (8), pp. 1363-1374.

93./ F. Shahrokhi, O. Sykora, L. A. Szekely and I. Vrto, k-planarcrossing numbers, Discrete Appl. Math. 155 (2007), 1106–1115.

94./ P. L. Erdos, A. Seress and L. A. Szekely, Non-trivial t-intersectionin the function lattice, Annals of Combinatorics 9 (2005) 177–187.

111

References

1. Li YS, Wang J Erdos-Ko-Rado-type theorems for colored sets ELEC-TRONIC JOURNAL OF COMBINATORICS 14 (1): Art. No. R1JAN 3 2007

95./ L. A. Szekely, Hua Wang, and Yong Zhang, Some non-existenceresults on Leech trees, Bull. Inst. Comb. Appl. 44 (2005).

References


96./ Linyuan Lu and L. A. Szekely, Using Lovasz Local Lemma inthe space of random injections, Electronic J. Comb. 14 (2007)R63, pp. 13.

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1. D. Scheder, P. Zumstein, Unsatisfiable CNF formulas need many con-flicts, Arxiv preprint arXiv:0806.1148, 2008

2. Heidi Gebauer, Robin A. Moser, Dominik Scheder and Emo Welzl, TheLovasz Local Lemma and Satisfiability, Efficient Algorithms LectureNotes in Computer Science, 2009, Volume 5760/2009, 30-54.

3. D. Scheder, P. Zumstein, How many conflicts does it need to be unsat-isfiable?, Lecture Notes In Computer Science, Proceedings of the 11thinternational conference on Theory and applications of satisfiabilitytesting, Guangzhou, China Pages: 246-256 2008.

4. D. Scheder, Unsatisfiable Linear CNF Formulas Are Large, and Diffi-cult to Construct Explicitely, 27th International Symposium on The-oretical Aspects of Computer Science - STACS 2010, Nancy : France(2010), 621-632

5. JULIA BOTTCHER, YOSHIHARU KOHAYAKAWA, AND ALDOPROCACCI, PROPERLY COLOURED COPIES AND RAINBOWCOPIES OF LARGE GRAPHS WITH SMALL MAXIMUM DEGREE,Arxiv preprint arXiv:1007.3767, 2010

97./ L. A. Szekely and Hua Wang, Binary trees with the largest num-ber of subtrees, Discrete Appl. Math. 155 (2007), 374-386.

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3. Yan, W., Yeh, Y. N., Enumeration of subtrees of trees, THEORETI-CAL COMPUTER SCIENCE 369 (1-3): 256-268 DEC 15 2006

4. Heuberger C, Wagner SG, Maximizing the number of independent sub-sets over trees with bounded degree Source: JOURNAL OF GRAPHTHEORY Volume: 58 Issue: 1 Pages: 49-68 Published: MAY 2008

5. The On-Line Encyclopedia of Integer Sequences, A092781.http://www.research.att.com/˜njas/sequences

6. C. Heuberger, H. Prodinger, On α-greedy expansions of numbers, Ad-vances in Applied Mathematics 38 (2007)505-525


98./ L. A. Szekely and Hua Wang, Binary trees with the largest num-ber of subtrees with at least one leaf, Congressus Numerantium177 (2005), 147–16.

References

1. Yan WG, Yeh YN Enumeration of subtrees of trees THEORETICALCOMPUTER SCIENCE 369 (1-3): 256-268 DEC 15 2006



99./ E. Czabarka, O. Sykora, L. A. Szekely and I. Vrto, Crossing num-bers and biplanar crossing numbers II: using the probabilisticmethod, Random Structures and Algorithms 33 (2008) 480–496.

References

1. Joshua K.Lambert, Finding a biplanar embedding of Cn×Cn×Cl×Pm

2. Joshua K.Lambert, The biplanar crossing number of Ck×Cl×C2m×Pn


4. Pach, J., Geometric graph theory. Surveys in combinatorics, 1999(Canterbury), 167–200, London Math. Soc. Lecture Note Ser., 267,Cambridge Univ. Press, Cambridge, 1999

100./ M. A. Steel and L. A. Szekely, Teasing apart two trees, Combi-natorics, Probability, and Computing 16 (2007) (6) 203–222.

113

References

1. M. Steel, CONSISTENCY OF BAYESIAN INFERENCE OF RE-SOLVED PHYLOGENETIC TREES, arXiv:1001.2864v1 [q-bio.PE]17 Jan 2010

2. Louxin Zhang, Jian Shen, Jialiang Yang and Guoliang Li, Analyzingthe Fitch Method for Reconstructing Ancestral States on Ultramet-ric Phylogenetic Trees, Bulletin of Mathematical Biology Volume 72,Number 7, 1760-1782, DOI: 10.1007/s11538-010-9505-8

3. Olivier Gascuela, and Mike Steel, Inferring ancestral sequences intaxon-rich phylogenies, Mathematical Biosciences Volume 227, Issue2, October 2010, Pages 125-135

101./ M. A. Steel and L. A. Szekely, On the variational distance of twotrees, ANNALS OF APPLIED PROBABILITY 16 (3): 1563-1575 AUG 2006

References


102./ D. Bokal, E. Czabarka, L. A. Szekely, and I. Vrto, Graph minorsand the crossing number of graphs, Electronic Notes in DiscreteMath.

References

1. Janos Pach, Jozsef Solymosi, Gabor Tardos, Crossing numbers of im-balanced graphs, Journal of Graph Theory Volume 64, Issue 1, pages1221, May 2010


3. GASPER FIJAVZ AND DAVID R. WOOD GRAPH MINORS ANDMINIMUM DEGREE, arXiv:0812.1064v1 [math.CO] 5 Dec 2008

4. D BOKAL, G FIJAVZ, DR WOOD -THE MINOR CROSSING NUM-BER OF GRAPHS WITH AN EXCLUDED MINOR Arxiv preprintmath.CO/0609707, 2006 - arxiv.org


103./ L. A. Szekely, An optimality criterion for the crossing number,Ars Mathematica Contemporena 1(2008), 32–37.

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References


2. M. J. Pelsmajer, M. Schaefer, D. Stefankovic, : REMOVING IN-DEPENDENTLY EVEN CROSSINGS, SIAM JOURNAL ON DIS-CRETE MATHEMATICS 24(2)(2010) 379–393.

3. M. J. Pelsmajer, M. Schaefer, D. Stefankovic, Crossing numbers ofgraphs with rotation systems Lecture Notes In Computer Science Pro-ceedings of the 15th international conference on Graph drawing, Syd-ney, Australia Pages: 3-12 , 2007 ISBN ISSN:0302-9743 , 3-540-77536-6

104./ A. Sali and L. A. Szekely, On the existence of Armstrong in-stances with bounded domains, Foundations of Information andKnowledge Systems (FoIKS 2008), Lecture Notes in ComputerScience Vol. 4932, pp. 151–157, 2008, Springer-Verlag.

References

1. Sven Hartmann, Uwe Leck and Sebastian Link, On Codd Familiesof Keys over Incomplete Relations, The Computer Journal AdvanceAccess published September 29, 2010

2. Sven Hartmann, Henning Kohler, and Thu Trinh, On the Existenceof Armstrong Data Trees for XML Functional Dependencies, S. Linkand H. Prade (Eds.): FoIKS 2010, LNCS 5956, pp. 94113, 2010.

105./ E. Czabarka, P. Dankelmann, L. A. Szekely, Diameter of 4-colorable graphs, Europ. J. Comb. 30 (2009) 1082–1089.

106./ M. A. Steel, L. A. Szekely, E. Mossel, Phylogenetic informationcomplexity: is testing a tree easier than finding it? J. Theor.Biology 25 (2009) 95–102.

References

1. Matthias Dehmer, Marina Popovscaia, Towards Structural NetworkAnalysis, BULETINUL ACADEMIEI DE STIINTE A REPUBLICIIMOLDOVA. MATEMATICA Number 1(62), 2010, Pages 322

107./ L. A. Szekely, Yiting Yang, On the expectation and varianceof the reversal distance, Acta Univ. Sapientiae, Mathematica 1(2009) (1) 5–20.

108./ E. Czabarka, L. A. Szekely, S. Wagner, The inverse problem forcertain tree parameters, Discrete Applied Math. 157(15)(2009),3314–3319.

115

109./ Hyunju Kim, Z. Toroczkai, I. Miklos, P. L. Erdos, L. A. Szekely,On realizing all simple graphs with a given degree sequence Phys.Lett. A Math. Theor. 42 (2009) 392001.

References

1. Del Genio CI, Kim H, Toroczkai Z, et al., Efficient and Exact Samplingof Simple Graphs with Given Arbitrary Degree Sequence, PLOS ONEVolume: 5 Issue: 4 (2010) Article Number: e10012

2. Erdos PL, Miklos I, Toroczkai Z, A simple Havel-Hakimi type algo-rithm to realize graphical degree sequences of directed graphs, ELEC-TRONIC JOURNAL OF COMBINATORICS 17 (1)(2010) ArticleNumber: R66

3. Klinkowski, AnyTraffic routing algorithm for label-based forwarding,IEEE GLOBCOM 2009 proceedings.

4. Charo I Del Genio, Hyunju Kim, Zoltan Toroczkai, Kevin E. Bassler,Efficient and exact sampling of simple graphs with given arbitrarydegree sequence

5. Ginestra Bianconi, Entropy of network ensembles, Physical ReviewE 79, 036114 (2009).

110./ M. A. Steel and L. A. Szekely, Inverting random functions III:discrete MLE revisited, Annals Comb. 13 (2009) 373–390.

References

1. M. Steel, CONSISTENCY OF BAYESIAN INFERENCE OF RE-SOLVED PHYLOGENETIC TREES, arXiv:1001.2864v1 [q-bio.PE]17 Jan 2010


111./ M. A. Steel, L. A. Szekely, An improved bound on the MaximumAgreement Subtree problem, Appl. Math. Letters 22 (2009)1778–1780.

References

1. J Goodrich, Phylogenetic Pipeline for the Detection of Horizontal GeneTransfer

112./ H. Aydinian, E. Czabarka, P. L. Erdos, L. A. Szekely, A tour ofM -part L-Sperner families, to appear in J. Comb Theory Ser A.

113./ H. Aydinian, E. Czabarka, K. Engel, P. L. Erdos, L. A. Szekely,A note on full transversals and mixed orthogonal arrays, Aus-tralasian J. Comb. 48(2010), 133–141.

116

114./ L. A. Szekely, Hua Wang, and Taoyang Wu, The sum of dis-tances between the leaves of a tree and the ’semi-regular’ prop-erty, Discrete Math. (2010)

115./ D. Bokal, E. Czabarka, L. A. Szekely, and I. Vrto, General lowerbounds for the minor crossing numbers of graphs, Discrete andComputational Geometry 44(2010), 463–483.

OTHER PUBLICATIONS

116./ Combinatorial exercises, JATE University, Szeged, l983 (in Hun-garian).

References

1. P. Hajnal Elementary problems in combinatorics, Polygon, BolyaiInstitute, Szeged, 1997 (in Hungarian).

117./ L. A. Szekely, Analytic Methods in Combinatorics, Thesis forthe Candidate’s Degree, Hungarian Academy of Sciences, 1985.(in Hungarian)

References

1. Boris Bukh, Measurable sets with excluded distances

2. Quas A, Distances in positive density sets in R-d, JOURNAL OFCOMBINATORIAL THEORY SERIES A Volume: 116 Issue: 4 Pages:979-987 Published: MAY 2009

118./ An algebraic approach to the uniform concurrent multicommod-ity flow problem: theory and applications, Technical Report CRPDC-91-4, Department of Computer Science, University of North Texas,1991 (with F. Shahrokhi).

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1. L Torok, Volumes of 3D Drawings of Homogenous Product Graphs(Extended Abstract),SOFSEM 2005: Theory and Practice of Com-puter Science: 31st Conference on Current Trends in Theory and Prac-tice of Computer Science Liptovsky’ Ja’n, Slovakia, January 22-28,2005. Proceedings, LNCS 3381/2005, p. 423. Editors: Peter Vojta’s(,Ma’ria Bielikova’, Bernadette Charron-Bost, et al.


3. P. Ruzicka, Efficient communication schemes, Theory and practice ofinformatics SOFSEM’98, Band 25, 244–263.

117

4. L. Stacho, I. Vrto, Bisection width of transposition graphs, DiscreteAppl. Math. 84 (1998), 221–235.

5. O. Sykora, I. Vrto, On crossing numbers of hypercubes and cube-connected cycles, BIT Comp. Sci. and Num. Math. 33(1993)232–237.



8. I. Vrto, 2 remarks on expanding and forwarding, Discrete Appl. Math.58 (1995) (1) 85–89.

9. D. Barth, F. Pellegrini, A. Raspaud, J. Roman, On bandwith, cutwidth,and quotient graphs, RAIRO — Informatique Theoretique et Ap-plications — Theoretical Informatics and Applications 29 (1995)(6), 487–508.

10. M.-C. Heydemann, Cayley graphs and interconnection networks,in: Algebraic Methods and Applications, eds. G. Hahn and G.Sabidussi, NATO ASI Series C Vol. 497, Kluwer, 1997, 167–224.

119./ M.A. Steel - L.A. Szekely - P.L. Erdos: The number of nucleotidesites needed to accurately reconstruct large evolutionary trees,DIMACS, Rutgers University, New Brunswick, New Jersey, USA1996. DIMACS Technical Reports 96-19

References


2. M. Farach, S. Kannan, Efficient algorithms for inverting evolution, J.ACM 46 (4) (1999), 437–449.


120./ L. A. Szekely, Zarankiewicz crossing number conjecture, arti-cle in: Kluwer Encyclopaedia of Mathematics, Supplement IIIManaging Editor: M. Hazewinkel Kluwer Academic Publishers,2002, 451–452.

References


121./ Other communications:

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2. G. Elekes, Circle grids and bipartite graphs of distance, Combinator-ica 15(1995), 167–174.

3. G. Chartrand, P. Erdos, O. R. Oellerman, How to define an irregulargraph? College Math. Journal 19(1988), 36–42.

4. G. J. Szekely, Contests in Higher Mathematics, Problem Books inMathematics, Springer-Verlag, 1995, p. 34, p.36.

5. S. Fajtlowicz, Written on the Wall, p. 67.

6. C. T. Edwards, Double-elimination tournaments: Counting and cal-culating, Am. Stat. 50(1996)(1), 27–33.


8. V Ro”dl, B Nagle, J Skokan, M Schacht, , and Y. Kohayakawa Thehypergraph regularity method and its applications, PNAS, June 7,2005 — vol. 102 — no. 23 — 8109-8113.

9. V Roedl, J Skokan, Counting subgraphs in quasi-random 4-uniformhypergraphs, Random Structures and Algorithms, 2005 Volume 26,Issue 1-2 , Pages 160 - 203

10. Ben Gum, The secretary problem with a uniform distribution

11. Rodl, V. Skokan, J. Applications of the regularity lemma for uniformhypergraphs. (English. English summary) Random Structures Algo-rithms 28 (2006), no. 2, 180–194.

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