图论在集合论中的应用

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1、山东大学硕士学位论文APPLICATIONSOFGRAPH咖ORYINSETTHEORyZhangXin国_sLofMath．&Sys．Sci．，ShandongUniv．，Jinan250100)AbstractGraphtheoryisacomponentofmathematics，whichismainlyaboutthestudyofgraphs．Thegraphingraphtheoryconsistsofasetofpointstogetherwithlinesjoiningcertainpairsofthesepoints．Thiskind

2、ofgraphisusuallyusedtodescribecertainrelationsofsomethings，inwhichpointsstandforthingsandlinesstandfortherelationsbetweenthethings．Oraphtheoryisapartofappliedmathematicsindeed,thusinhistoryithasbeenestablishedbymanymathematiciansrespectively．TheearHestknownpaperongraphtheoryappea

3、redintheworksofEulerin1736，whichconsideredtheprimitiveproblemsthathadstrongpracticalbackground．GraphtheoryderivedfromfamousproblemofthesevenbridgesofK6nigsberg(s∞【1】)．Eulersolvedthisproblemin1736．Hechangedthisproblemintothefirstgraphtheoryproblembyabstractanalyzedmethod．Eulerprov

4、edthatthisproblemhadnosolutions．Moreover,heextendedthisproblem．ThisjobmadeEulerbecomethesponsorofgraphtheory(andtopology)．Theextensiveapplicationsofgraphtheoryhavepromoteditsowndevelopment．From1940sto1960ssometheoriesaboutgraphssuchasmalroidtheory、hypergraphtheory、polargraphtheor

5、y、algebraicgraphtheoryandtopologicalgraphtheory(see【2—8])haddevelopedgreatly．Settheoryhasbec．．omeasubjectsincethelate19thcentury．From1874to1897thesponsorofthetheory0．Cantorproposedaseriesofthesethatgavethefoundationofsettheory．Sincethen,theconceptsandresultsofthetheoryhavebeenapp

6、liedinalmosteverycomponentofmathematics,whichhaveinfluencedmathematicsdeeply．TheoutcomeofCantor’ssettheorygaverisetogreatreflectioninthefieldof4山东大学硕士学位论文matlacmatiesatthattime．ItmsapprovedandpraisedgreatlybysomcmathematieiamsuchasILDedekind,B．Russell，D．Hilbert,andSOOn_Itwasalsos

7、tronglyopposedbysolnemathematiciansespeciallyL．Kroneeker．Sincethelateof19tlacentury,variousparadoxeshadappearedcontinuallyandatthattimesuelaparadoxeseouldn’tbeansweredap])lyingsettheory．InordertoremedyCantor'stheory,in1908E．Zermelogavethefirstaxiomofsettheory(see【9】【10】)．Theseaxi

8、omsmakeitclearthatwhatisreasonabletodeal