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图论引论

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作者：B.Bollobas 著

出版社：世界图书出版公司

出版时间：1999-11-1

I S B N： 9787506200936

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图论引论

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图论引论（英文版）

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29.00元

图论引论（影印版）

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This book is intended for the young student who is interested in graph theory and wishes to study it as part of his mathematical education. Experience at Cambridge shows that none of the currently available texts meet this need. Either they are too specialized for their audience or they lack the depth and development needed to reveal the nature of the subject.

　　本书为英文版。

内容简介

片断：
CHAPTER1
Fundamentals
Thepurposeofthisintroductionistofamiliarisethereaderwiththebasic
conceptsandresultsofgraphtheory.Thechapterinevitablycontainsa
largenumberofdefinitionsandinordertopreventthereadergrowing
wearyweprovesimpleresultsassoonaspossible.Thereaderisnotexpected
tohavecompletemasteryofChapter1beforesamplingtherestofthe
book,indeed,heisencouragedtoskipaheadsincemostoftheterminology
isself-explanatory.Weshouldaddatthisstagethattheterminologyof
graphtheoryisfarfrombeingstandard,thoughthatusedinthisbookis
wellaccepted.
?Definitions
AgraphGisanorderedpairofdisjointsets(V,E)suchthatEisasubset
ofthesetofunorderedpairsofV.Unlessitisexplicitlystatedotherwise,we
consideronlyfinitegraphs,thatisVandEarealwaysfinite.ThesetVis
thesetofverticesandEisthesetofedges.IfGisagraphthenV=v(G)
isthevertexsetofGandE=E(G)istheedgeset.Anedge{x,y}issaidto
jointheverticesxandyandisdenotedbyxy.Thusxyandyxmeanexactly
thesameedge;theverticesxandyaretheendverticesofthisedge.IfxyeE(6)
thenxandyareadjacentorneighbouringverticesofGandtheverticesx
andyareincidentwiththeedgexy.Twoedgesareadjacentiftheyhave
exactlyonecommonendvertex.
Astheterminologysuggests,wedonotusuallythinkofagraphasan
orderedpair,butasacollectionofverticessomeofwhicharejoinedby
edges.Itisthenanaturalsteptodrawapictureofthegraph.Infact,some-
timestheeasiestwaytodescribeagraphistodrawit;thegraphG=
({1,2,3,4,5,6},{12,14,16,25,34,36,45,56})isimmediatelycomprehended
bylookingatFigure1.1.
WesaythatG'=(V',E')isasubgraphofG=(V,E)ifV'Vand
E'E.InthiscasewewriteG'G.IfG'containsalledgesofGthatjoin
twoverticesinV'thenG'issaidtobethesubgraphinducedorspannedby
V'andisdenotedbyG[v'].AsubgraphG'ofGisaninducedsubgraphif
G'=G(G')].IfV'=V,thenG'issaidtobeaspanningsubgraphofG.
TheseconceptsareillustratedinFigure1.2.
Weshalloftenconstructnewgraphsfromoldonesbydeletingoradding
someverticesandedges.IfWv(G)thenG-W=G[V\W]isthesub-
graphofGobtainedbydeletingtheverticesinWandalledgesincidentwith
them.SimilarlyifE'E(G)thenG-E'=(v(G),E(G)\E').IfW={w}
andE'={xy}thenthisnotationissimplifiedtoG-wandG-xy.
Similarly,ifxandyarenon-adjacentverticesofGthenG xyisobtained
fromGbyjoiningxtoy.

作者简介

Chapter Ⅰ Fundamentals
1.Definitions
2.Paths， Cycles and Trees
3.Hamilton Cycles and Euler Circuits
4.Planar Graphs
5.An Application of Euler Trails to Algebra
Exercises
Notes
Chapter Ⅱ Electrical Networks
1.Graphs and Electrical Networks
2.Squaring the Square
3.Vector Spaces and Matrices Associated with Graphs
Exercises
Notes
Chapter Ⅲ Flows， Connectivity and Matching
1.Flows in Directed Graphs
2.Connectivity and Menger‘s Theorem
3.Matching
4.Tutte's 1-Factor Theorem
Exercises
Notes
Chapter Ⅳ Extremal Problems
Chapter Ⅴ Colouring
Chapter Ⅵ Ramsey Theory
Chapter Ⅶ Random Graphs
Chapter Ⅷ Graphs and Groups
Subject Index
Index of Symbols