KO 28.10.16

fah-2.LI [ Saia a MENTER, qnihkt, bogeudijunht ]

Sind D= ( V,A) ein Digraph

,Ste V

und KEN,

so gilt :

Es gilt geuan dam k bogeudijuuhist .

Uge in D,

an esfnjedeTeenage RSA ur 1121 £ k . I

even st . Ug in A 'R gin .

Bend . Sind U, ,

. .

,Un e- A st - Uye ul

Winwj =P titj,

so gilles offuidlthfur jedes Ret in 't IR Kk . l in

ie Ltd wit Win R = ¢.

• Get es uugekehul fin alle REA ul

1121£ b- I even st -

Wyin A- R

.

• Daun gin es in Nehherk (D ,n ) ml

n = 1in kin $EVmrsef'

und t¢$und

u( such )= 1M$11 -4-1.

• Da n gaenahlj ,ist also die minimal

wkapanileit ewes st - Schultes in D winelesku )

k.

. Nad Sat 2.16 ( Max . Hoo - th . Gttleoeu )

gilt es also ein st - Thssfoouhkrte;had Sak 2. A henna we auaehueu

,does

f- EINA,also (ugeu u= Aa ) fete , igtirt .

• Dehompouen man f lie in Sak 2.18

in st . Wey P und Kuse C ul

gauttehljem w,so it w(P)=l

fr Ile PEP ; wgea vallfkhalso IPI =L

.

• Da u = Ha and die Uye in P

bogeadsjnnkt . #

Altrualiufrmtvnydahe .19

Die maximal Antell won bogeadsjuuhks

st .

Wgeu ist gle 'd do minimal

kardinaltat ew Bgeaueye ,uad dem

Cutting kin st -

Uy web aishit .

Enter gin es k loges - dshukk

st -

Wege odr es gilt < k Bogen ,

nad dena Eatfmuy bin set Ugwell ewskvt ( ah wdt bids )

.

Sak 2.21

÷d G= (Vi E) en Graph ,ste V and

keln,so gilt : Es gin gun

dam

k hauteudsjuuhk st -

Wege in G,

weu es

fu jede Teenage FEE nil IFI < let

even st . Wg in Gltgim .

Being Folgt an Sak 2.19-

µ@-@ m ) @~@

sah-2.22L.netG= (V. E) en Graph ,

Ste V and

keln,so gilt : Es gilt gun

dam

kkuoteudsjuukk( af insimdt)st - Wye

inG,

Wen es fun jede TeenageTia Vi { s ,t } we Kr Kh . '

linen st . Ug in Giw gin .

But : Ibp an , Sah. 2.19

.

r in*@ Y¥F¥€

.

W@koollar2.24EinCpephG-AiE1mh1vl72istgeuanokuak-fadkauteu-2nsawwealayeudgweunes2nsdnujeoknPears.t

e V

( s±t ) weighs k kaukadsjuhk At - Ugegtk .

kaollar

2.25¥ G = (v. E) mh

lvbkit

geuandear k - fad

kuotentusawwealayeud,

wean es trisdnu jeokn Pear site V

( s±t ) weighs khuokadsjuhkAt -Ugegi1 0 u=1

µ4 , tyoyo .

1 7�1�

°