Modern Graph Theory

412 Pages·2002·5.55 MB·English

by  Bela Bollobas

BelaB ollobas
Modern
GraphT heory
�Springer
18 4
GraduTaetxet isnM athematics
EditoBroiaarld
S.Ax lerF. W. GehringK .AR.i bet
GraduaTteex tisnM athematics
TA KEUTIIZARIINnGt.r odtuoc tion 34 SPITZPERr.i ncoifRp alnedsWo aml k.
AxiomSaetTtih ce o2rnyed.d . 2nedd .
2 OXTOBYM.e asaunrCdea teg2onredyd .. 35 ALEXANDERIWERSMeEvR.eC roamlp lex
3 SCHAEFETRo.p oloVgeicctSaoplra ces. VariaabnlBdea sn aAclhg eb3rreadds ..
2nedd . 36 KELLEYINAMIOKA eLitn aelar.
4 HILTON/STAMMABA CCoHu. risne TopoloSgpiaccaels .
HomoloAgligcea2blnr edad .. 37 MONKM.a themLaotgiicca.l
5 MAC LANEC.a tegfoortrih Weeos r king 38 GRAUERTIFRITSZeSvCeCHroEam.lp lex
Mathema2tniedcd i.a n. Varbilaes.
6 HUGHES/PIPPrEjoRce.t iPvlea nes. 39 ARVESOANn.I nvittaoCt *i-oAnl g.e bras
7 J.-SEPR.R EA. C ourisnAe r ithmetic4.0 KEMENYISNELLIKDNAePnPu. merable
8 TA KEUTIIZARAINxGi.o mSaetTtih ce ory. Markov C2hneaddi .n s.
9 HUMPHREYISn.ot dructtoiL ioAenl gebra4s1 APOSTOMLo duFluanrc tainodn s
anRde preseTnhteaotriyo.n DiriScehrliienNet us m bTheero ry.
10C oHENA. C ourisnSei p mlHeo motopy 2nedd .
Theory. 42 J.-SPE.RRE .L inReeaprr eseonft ations
CoNWAYF.u nctoifOo nneCs o mplex FienG irtoups.
II
VariIa2.bn leded . 43 GILLMANIJERRIiSnOoNg.fCs o ntinuous
12B EALAS.d vanMcaetdh emAantaiclayls is.F unctions.
13A NDERSON/FURLLiEnRag.n sCd a tegori4e4s K ENDIEG.l emeAntlagreybG reaoimce try.
ofM odul2ensed.d . 45 LoEVE.P roibalyTbi hteoIr4.yt e hd .
14G oLUBITSKY/GuiSLtLEaMMbIalN.pe p ing4s6 LoEVE.P robbiaylT ihteoIrI4y.t e hd .
anTdh eSinirg urliaties. 47 MOISEG.e omeTtorpiocli ong y
15B ERBEIRANLe.c tuirFneus n ctional Dimens2ai no3dn. s
AnasliaysnO dp eraThteoorr y. 48 SACHs/GWeun.eR realla tfiovri ty
16W INTETR.h Set rucotfFu ireel ds. Mathematicians.
17R osENBLARTaT.n dPormo ce2snseded s.. 49 GRUENBERG/WLEiIRn.e ar Geometry.
18H ALMOSM.e asuTrhee ory. 2nedd .
19H ALMOSA. H libeSrptaP creo bBloeomk . 50 EDWARDFSe.r mLaatsT'thse orem.
2nedd . 51 KLINGENBERAG C.o urisnDei f freential
20 HUSEMOLLFEiR.bB ruen d3ldree sd.. Geometry.
21 HUMPHREYLSi.n Aelagre bGrraoiucp s. 52 HARTSHORANEl.g ebGreaoimce try.
22 BARNES/MAAnCA Kl.g ebIrnatuircco tnd io53 MANINA. C ourisnMe a themaLtoigciacl.
toM athemaLtoigciacl. 54 GRAV ERIWA TKINSC.o mbinawtiotrhi cs
23 GREUBL.i nAelagre 4btrehad .. Emphaosnti hsTe h eoorfGy r aphs.
24 HoLMESG.e ometric AFnuanlcytsiio5sn5 a BlR oWN/PEARICnYo.td rucntt oOi poerator
anIdt Asp plications. TheoryE lemeonfFt usn ctAinoanilasyls.
1:
25 HEWITT/STROMRBeERaaGln.A db stract5 6 MASSAElYg.e bTroapioclA ong y:
Anaylsis. Introduction.
26 MANESA.l gebTrhaeiocr ies. 57 CROWELL/FoIxn.t rodtuoKc ntoito n
27 KELLEGY.e neTroaplo logy. Theory.
28 ZARISKIISAMCUoELm.m utAaltgievber a.5 8 KoBLITpZ-.ai dNcu mbers, p-adic
Vol.!. Anailysas,nZ de ta-Fu2nncedtd i.o ns.
29 ZARISKIISAMCUoELm.m utAaltgievber a.5 9 LANGC. yclotFoimeilcd s.
Vol.!!. 60 ARNOLDM.a themMaettihciaonld s
30 JACOBSOLNe.c tiunArb esst ArlagcetIb .r a ClaiscMsaelc ha2ninecdds ..
BasCiocn cepts. 61 WHITEHEAEDl.e meonfHto sm otopy
31J ACOBSOLeNc.t uirAnebs s tArlagcetIb Ir.a Theory.
LinAelagre bra. 62 KARGAPOLOV/MERLZJAFKuOnV.d amentals
32 JACOBSLeONc.t uirnAeb ss tArlagcetb ra oft hThee oroyfG roups.
IIThIe.o royfF iealndGdsa lTohieso ry.6 3 BOLLOBAGSr.a Tphhe ory.
33 HIRSCDHi.f freenTtoipaoll ogy.
(contaifnituneedrde x)
BelBao llobas
ModernG rapThh eory
With1 18F igures
�Springer
BelBao llobas Trinity College
DepartmoefnM ta thematSicciaeln ces UniverosfiC taym bridge
UniverosfiM teym phis CambridCgBe2 TQ
I
37 25N orriswood UnitKeidn gdom
MemphisT,N 38152 bb.o [email protected] m.ac.
USA
[email protected]
EditorBioaalr d
S.A xler F.WG.e hring K.AR.i bet
MathematDiecpsa rtmentM athematDiecpsa rtmentM athematDiecpsa rtment
SanF ranciSstcaot e EasHta ll UniverosfiC tayl ifornia,
University UniverosfiM tiyc higan atB erkeley
SanF ranciCsAc o9,4 132 AnnA rboMrI,4 8109 BerkelCeAy 9,4 720-3840
USA USA USA
MathematSiucbsjc etC lassific(a2t0i0o00n)5 :- 0015,C xx
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Bollobas, Bela.
Modergnr apthh eorBye lBao llobas.
I
p. em-. (Gradutaetxeit nsm athema;t 1i8c4s)
Inclubdiebsl iographical( pr.-e fe)ar nedni cnedse x.
ISB9N78 -0-387-98I4S88B9-N798 -1-4612(-e06B1o9o-k4 )
DOl1 0.1007/978-1-4612-0619-4
acid-fpraepee r)
GrapThh eory. Seires.
I. I.T itlIeI..
QAI66.B66139 98
511."5 -dc21 98-11960
ISBN9 78-0-387-98488-9 Printoenad c id-fpraepee r.
© 199S8 priSncgieern ce+MBeudNsieiawYn oersks
Originalpluyb lbiySs phrinedg Serc ienBcusinee+s sM edia, Incin. 1 998
Allr ighrtess ervTheids.w orkm ayn otb et ranslaotrec do pieidnw holoer i np art
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andr atphmieid x oiMfnar gk ocvhi anAsn.o tihmepro crotnannetwc ept rieosne nt
ibse twtehTueetn tp eo lynoofamg iraatlph phear, t iftnuicotnoi ftoh neso retical
pyhsiacnthsde,p owenrefkwun lpo otl ynomials.
Thdee epeannbdir noga doetfnh sibeune jgci tn dibcyaa ltled det vheel opments
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Thearreea g reats imgannioyfip cepanrn otb wlheimarcsih sn ea tuirnthal el y
sujbemcatn:oy ft hearsese i mtposl teaa tnledo ionkn obcuaretenp tr ovtion g
bes urprhiastrirodn e gsloIyilt nsv oe c .o inctihdPaeatnEu crled t ohsge,r eatest
probletmh-weop rohlsaedesv r se ere n, mduecovhhfo i ttsie tmdgoe r atphhe ory.
Thiasm azwienagol fot phe pnr obilmseo mssat b llye sbsuiatsnl ogt,,os ome
extaec nutrA,sb el.e ssintgh,ei rasbce eo canansfluttos owefe x ciptrionbgl ems
stimutlhaet idnegvo etflh soeujp cbmetaec: nu trb seec,ap uesocepa lbneem isled
inwtoor koinsn hga loldroe wa dp-reonbdwl heimwcshh ib,le eari ans gu perficial
resemtbiolm epnocprert oabndltoe mrnseo,aat ld lvyat nhsceuje cbe t.
Icno ntrtamoso ttrs atd itbiroannoacmflha etsh iecmfsaoa,ttr horgoruoguhn d­
iniggn r atphhe aobrsyo,tr hbreie nsgaun lpdtr soi oosfn shl ayol ftfh bea tIttl e.
irsar thea tg ean uinei gnpr ratophbhel coearmbny es olbvyse idm applpyl ying
ane xisting thfreoomgr reatmph,he ooerfrri oytm oh uetrsM iodrteey. p ically,
solvap irnogb rleeqmua i" rbearhsea nardgsu"m ent wtioatkg hne otrwhene­ r
suwlthti nae tww iMsotro.ef ttehnna onit tt,u rnosuth ta nto neth eeo xfi sting
higohw-epmraecdh ionfmea rtyh ecmisoas fat niy thuoe sal,npn d e vheerlate ss
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thseu abnsttpiraolb olfe mstsuh bejr eacttthhe,tar bon u imladc hifnoiertor swy n
sake.
Hopefthuerl elaywd,ie alrpl p retchbieea atauents dyi gniofiftc hamenaj coer
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propoorftti hoeAnml .th osuogmohef t heex erarceis streasi ghtmfoosortfw ard,
thems uarbes taannsdto miweais lltr,le etvctehhn me o satbr leea der.
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ando bavnil oiounfaset ktA.as cs ucthhar,ee ya ktimon a nayp robilgrne pamh
thetohrseyoi:rl uitlsii okner leyq iutniogr eean nuodir tiygt ihnoauTlgh huttsh. e
expegrtaiisinesne o dl tvhieenx ge rictnih siess botopoka dyii sv ilndioektne dlsy
onilgnyr atphhea onrodyt hberra nocmfha etsh iecmbsaua,ttl isno other scientific
discsi.p line
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B. B.
Memphis
Marc1h,5 1 998
Preface
Gratphhe ioasry yo ubnurgta pmiadtluysr ujicbentEg.v ednu ritnhgqe u arotfe r
ac enttuhIral yte ctouniri tenC da mbriictdh gaenc,go eindds eraanbIdhl ayv,e
foutnhdtha etri easc lenaerfe odar t ext iwnhtriocdthuhr ceee asnd oeotrn ly to
thwee ll-esrteasbulltitmossa h,noe ytfdb h nueet w deerv eloapswm ee.lIn ltt si s
hoptheadtht i s volguosm oemw eawt yio lwlars dast ithsafntye iendg.
Theirtseo m ou ch fhoaers r ienc golueHr oswee.thv eerrare,em anwya yosf
usitnhbgeo ofkoar s ingmleesc-toseuerar fstaee :rl p irtetplareaa ntcyih oanp ter
cabnei ncliutndh meead t erbieca olv etroe d.s trlAisylcptht eoautkghihearn rege
almnooms att hempareteqiruciatslhis etu ebmjsae,tc attne drp athocethfe e b ook
demamnadt hemmaattiufcrraiotltmh syu et ed nt.
Eacohtfh teec nh apctoesnrtsossiaf b ofiuvstee cttioognewsti,hats e her l ection
oefx eracnisdso emse, g briabplnhioeiotscI.atnl h o ep ensiencgto ifaco hnasp ter
thmea teirisin atrlo ducemdu coghfte h tneit rmleeys :aru elr tasts hiemrap nlde ,
thper osao rfe priends eetnTathileelad .ts eerc tariemo onrsse p eciaanldi zed
procaeatbe rdi psak:cet erht eh eotreetnmbods ed eeapnetdrh perirow ohfisc,h
aren oatl wsaiymsap rlee ,rg aipviTedhnle syse.ec tiaroefn othsre r eader whose
intietrnhe teso tph iabcse eexnc ited.
Wed on oatt tetmogp itav nee xhaulsiotsftit hv eeo bruehtmo spt,eos how
hotwh e rceosmtueol gtetsto fh oerarmc ohetshievIoenro yr.dt eopr r eserve
thfers ehnaensedsl egoathfne mc aet etrhpiera els,e innsto aottv ieorn-i p:ce dant
occastihorene aalidlesexy rp etcoft oerdim zaselo mdee toafti hlaesr gument.
Througthhobeuo tot khr ee awdiedlril s ccoovnenre wcittvihao rniosot uhse r
branocfmha ethse imcalsti,ok pet imtihzeagotrrioyou,np mtahtreaiolxrg ye,b ra,
probatbhieloirtyay,n k dnl ootg iAtclh,te hotorhuyeg. h ri nesoa etdx epret cot ed
haiven tikmnaotwelo etfdh gefiese sela, dm odaecsqtu aiwnittthahen wmco eu ld
enhatnhecejne o ymoetfnh btio so k.
Thbei bliongortaareepfs haf irrc oeahmxal u stwiearv ece ar:e ifuonlu art tribu­
tioontfsh m eaj ror esbuulbtte sy,to hnwadedt o l imtotrlteeh g ainsv ueg gestions
fofru rrtehiaendrg s.
Av ifteaalot tfurh beeo oitksh iactto nthauinndsor fee xdcesir .sS emosear e
vesryi mapnled, t ethseut n doenrlsyot ftha enc doinncbgeu ptt sgm,oaw nayy