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1、ReinhardDiestelGraphTheoryElectronicEdition2005cSpringer-VerlagHeidelberg,NewYork1997,2000,2005Thisisanelectronicversionofthethird(2005)editionoftheaboveSpringerbook,fromtheirseriesGraduateTextsinMathematics,vol.173.Thecross-referencesinthetextandinthem
2、arginsareactivelinks:clickonthemtobetakentotheappropriatepage.Theprintededitionofthisbookcanbeorderedviahttp://www.math.uni-hamburg.de/home/diestel/books/graph.theory/wherealsoerrata,reviewsetc.areposted.Substantialdiscountsandfreecopiesforlecturersareav
3、ailableforcourseadoptions;seehere.PrefaceAlmosttwodecadeshavepassedsincetheappearanceofthosegraphthe-orytextsthatstillsettheagendaformostintroductorycoursestaughttoday.Thecanoncreatedbythosebookshashelpedtoidentifysomemainfieldsofstudyandresearch,andwilld
4、oubtlesscontinuetoinfluencethedevelopmentofthedisciplineforsometimetocome.Yetmuchhashappenedinthose20years,ingraphtheorynolessthanelsewhere:deepnewtheoremshavebeenfound,seeminglydisparatemethodsandresultshavebecomeinterrelated,entirenewbrancheshavearisen.
5、Tonamejustafewsuchdevelopments,onemaythinkofhowthenewnotionoflistcolouringhasbridgedthegulfbetweeninvari-antssuchasaveragedegreeandchromaticnumber,howprobabilisticmethodsandtheregularitylemmahavepervadedextremalgraphtheoryandRamseytheory,orhowtheentirely
6、newfieldofgraphminorsandtree-decompositionshasbroughtstandardmethodsofsurfacetopologytobearonlong-standingalgorithmicgraphproblems.Clearly,then,thetimehascomeforareappraisal:whatare,today,theessentialareas,methodsandresultsthatshouldformthecentreofanintro
7、ductorygraphtheorycourseaimingtoequipitsaudienceforthemostlikelydevelopmentsahead?Ihavetriedinthisbooktooffermaterialforsuchacourse.Inviewoftheincreasingcomplexityandmaturityofthesubject,Ihavebrokenwiththetraditionofattemptingtocoverboththeoryandappli-cat
8、ions:thisbookoffersanintroductiontothetheoryofgraphsaspartof(pure)mathematics;itcontainsneitherexplicitalgorithmsnor‘realworld’applications.Myhopeisthatthepotentialfordepthgainedbythisrestrictioninscopewillservestudentsofco
