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1998, XIV, 394 p. 114 illus.
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B. Bollobas
Modern Graph TheorySeries: Graduate Texts in Mathematics, Vol. 184
The time has now come when graph theory should be part of the education of everyserious student of mathematics and computer science, both for its own sake and toenhance the appreciation of mathematics as a whole. This book is an in-depth accountof graph theory, written with such a student in mind; it reflects the current state of thesubject and emphasizes connections with other branches of pure mathematics. Thevolume grew out of the author's earlier book, Graph Theory -- An Introductory Course,but its length is well over twice that of its predecessor, allowing it to reveal many excitingnew developments in the subject. Recognizing that graph theory is one of severalcourses competing for the attention of a student, the book contains extensive descriptivepassages designed to convey the flavor of the subject and to arouse interest. In additionto a modern treatment of the classical areas of graph theory such as coloring, matching,extremal theory, and algebraic graph theory, the book presents a detailed account ofnewer topics, including Szemer'edi's Regularity Lemma and its use, Shelah's extension ofthe Hales-Jewett Theorem, the precise nature of the phase transition in a random graphprocess, the connection between electrical networks and random walks on graphs, andthe Tutte polynomial and its cousins in knot theory. In no other branch of mathematics isit as vital to tackle and solve challenging exercises in order to master the subject. To thisend, the book contains an unusually large number of well thought-out exercises: over 600in total. Although some are straightforward, most of them are substantial, and others willstretch even the most able reader.