随机图（第2版）

图书标准信息

• 作者 B.Bollobas 编
• 出版社 世界图书出版公司
• 出版时间 2003-10
• 版次 2
• ISBN 9787506265522
• 定价 75.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 498页
• 正文语种 英语

【内容简介】

　　Theperiodsincethepublicationofthefirsteditionofthisbookhasseenthetheoryofrandomgraphsgofromstrengthtostrength.Indeed，itsappearancehappenedtocoincidewithawatershedinthesubject;theemergenceinthesubsequentfewyearsofsingnificantnewideasandtools，perhapsmostnoteablyconcentrationmethods，hashadamajorimpact.Itcouldbearguedthatthesubjectisnowqualitativelydifferent，insofarasresultswhichwouldpreviouslyhavebeeninaccessiblearenowregardedasroutine.Severallongstandingissueshavebeenresolved，includingthevalueofthechromaticnumberofarandomgraph$G-{n，p}$，theexistenceofHamiltoncyclesinrandomcubicgraphs，andpreciseboundsoncertainRamseynumbers.Itremainsthecase，though，thatmostofthematerialinthefirsteditionofthebookisvitalforgaininganinsightintothetheoryofrandomgraphs.

【目录】

Preface
Notation
1ProbabilityTheoreticPreliminaries
1.1NotationandBasicFacts
1.2SomeBasicDistributions
1.3NormalApproximation
1.4Inequalities
1.5ConvergenceinDistribution
2ModelsofRandomGraphs
2.1TheBasicModels
2.2PropertiesofAlmostAllGraphs
2.3LargeSubsetsofVertices
2.4RandomRegularGraphs
3TheDegreeSequence
3.1TheDistributionofanElementoftheDegreeSequence
3.2AlmostDeterminedDegrees
3.3TheShapeoftheDegreeSequence
3.4JumpsandRepeatedValues
3.5FastAlgorithmsfortheGraphIsomorphismProblem
4SmallSubgraphs
4.1StrictlyBalancedGraphs
4.2ArbitrarySubgraphs
4.3PoissonApproximation
5TheEvolutionofRandomGraphs-SpareComponents
5.1TreesofGivenSizesAsComponents
5.2TheNumberofVerticesonTreeComponents
5.3TheLargestTreeComponents
5.4ComponentsContainingCycles
6TheEvolutionofRandomGraphs-theGiantComponent
6.1AGapintheSequenceofComponents
6.2TheEmergenceoftheGiantComponent
6.3SmallComponentsafterTime
6.4FurtherResults
6.5TwoApplications
7ConnectivityandMatchings
7.1TheConnectednessofRandomGraphs
7.2Thek-GonnectednessofRandomGraphs
7.3MatchingsinBipartiteGraphs
7.4MatchingsinRandomCraphs
7.5ReliableNetworks
7.6RandomRegularGraphs
8LongPathsandCycles
9TheAutomorphismGroup
10TheDiameter
11Cliques，IndependentSetsandColouring
12RamseyTheory
13ExplicitConstructions
14Sequences，MatricesandPermutations
15SortingAlgorithms
16RandomGraphsofSmallOrder
References
Index