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1、ReinhardDiestelGraphTheoryElectronicEdition2005cSpringer-VerlagHeidelberg,NewYork1997,2000,2005Thisisanelectronicversionofthethird(2005)editionoftheaboveSpringerbook,fromtheirseriesGraduateTextsinMathematics,vol.173.Thecross-referencesinthetextandinthemarginsareactivelinks:clickonthemtobet
2、akentotheappropriatepage.Theprintededitionofthisbookcanbeorderedviahttp://www.math.uni-hamburg.de/home/diestel/books/graph.theory/wherealsoerrata,reviewsetc.areposted.Substantialdiscountsandfreecopiesforlecturersareavailableforcourseadoptions;seehere.PrefaceAlmosttwodecadeshavepassedsinceth
3、eappearanceofthosegraphthe-orytextsthatstillsettheagendaformostintroductorycoursestaughttoday.Thecanoncreatedbythosebookshashelpedtoidentifysomemainfieldsofstudyandresearch,andwilldoubtlesscontinuetoinfluencethedevelopmentofthedisciplineforsometimetocome.Yetmuchhashappenedinthose20years,ingra
4、phtheorynolessthanelsewhere:deepnewtheoremshavebeenfound,seeminglydisparatemethodsandresultshavebecomeinterrelated,entirenewbrancheshavearisen.Tonamejustafewsuchdevelopments,onemaythinkofhowthenewnotionoflistcolouringhasbridgedthegulfbetweeninvari-antssuchasaveragedegreeandchromaticnumber,h
5、owprobabilisticmethodsandtheregularitylemmahavepervadedextremalgraphtheoryandRamseytheory,orhowtheentirelynewfieldofgraphminorsandtree-decompositionshasbroughtstandardmethodsofsurfacetopologytobearonlong-standingalgorithmicgraphproblems.Clearly,then,thetimehascomeforareappraisal:whatare,toda
6、y,theessentialareas,methodsandresultsthatshouldformthecentreofanintroductorygraphtheorycourseaimingtoequipitsaudienceforthemostlikelydevelopmentsahead?Ihavetriedinthisbooktooffermaterialforsuchacourse.Inviewoftheincreasingcomplexityandmaturityofthesubject,Ihavebrokenwiththetraditionofattempt
7、ingtocoverboththeoryandappli-cations:thisbookoffersanintroductiontothetheoryofgraphsaspartof(pure)mathematics;itcontainsneitherexplicitalgorithmsnor‘realworld’applications.Myhopeisthatthepotentialfordepthgainedbythisrestrictioninscopewillservestudentsofco
