图的因子和匹配可扩性

图书标准信息

• 作者 于青林、刘桂真 著
• 出版社 高等教育出版社
• 出版时间 2009-07
• 版次 1
• ISBN 9787040257588
• 定价 69.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 353页
• 字数 450千字

【内容简介】

GraphFactorsandMatchingExtensionsdealswithtwoimportantbranchesofgraphtheoryfactortheoryandextendablegraphs.Duetothematuretechniquesandwiderangesofapplications，factorsandmatchingsbecomeusefultoolsininvestigationofmanytheoreticalproblemsandpracticalissues.Thisbookincludesbasictechniques，theoreticalfoundations，aswellasrecentadvancesinthefield.Italsodiscussesopenproblemsandconjecturestoinspirethereaders.
Thisbookisprimarilyaimedatresearchersandgraduatestudentsingraphtheoryandcombinatoricsingeneral.However，allthenecessaryprerequisitesaredevelopedfromscratchandshouldbeaccessibletoupperlevelundergraduatestudentswithpriorknowledgeofgraphtheory.

【目录】

1MatchingsandPerfectMatchings
1.1Definitionsandterminologies
1.2Matchingsinbipartitegraphsandaugmentingpath
1.3Matchingsinnon-bipartitegraphs
1.4Sufficientconditionsfor1-factors
1.5Gallai-EdmondsStructureTheorem
1.6Numberof1-factors

2DegreeConstraintFactors
2.1Characterizationsoffactors
2.2Factorsinbipartitegraphs
2.3Factorswithspecialproperties
2.4L-factor

3FactorsandGraphicParameters
3.1Toughnessandk-factors
3.2Toughnessand[a，b]-factors
3.3Bindingnumberandfactors
3.4Connectivityandfactors
3.5Otherparametersandexistenceoffactors

4ComponentFactorsandConnectedFactors
4.1Starfactor
4.2Pathandcyclefactors
4.3El-ZaharsConjectureandothercomponentfactors
4.4Connected[a，b]-factors
4.5Connected（g，f）-factors
4.6Generalizedtrees

5ElementaryGraphsandDecompositionTheory
5.1Elementarygraphsand1-extendablegraphs
5.2Eardecomposition
5.3Minimalgraphsandmoredecompositions
5.4Bricksandoptimaleardecomposition

6k-ExtendableGraphsandn-Factor-CriticalGraphs
6.1Characterizationsandbasicproperties
6.2Equivalenceandrecursiverelationships
6.3Matchingextensionandgraphicparameters
6.3.1Matchingextensionandforbiddensubgraphs
6.3.2Matchingextensionandtoughness
6.3.3Matchingextensioninplanargraphsandsurfaces
6.3.4Matchingextension，degreesumandclosureoperations
6.3.5Matchingextensionandproductofgraphs
6.3.6Matchingextensionandotherparameters
6.4Extendabilityofsymmetricgraphs

7Extremalk-ExtendableGraphsandGeneralizations
7.1Maximalandminimalk-extendablegraphs
7.2Generalizationofmatchingextension
7.3Variationsofgraphextension

8FractionalFactorsofGraphs
8.1Fractionalmatchings
8.2Fractional（g，f）-factors
8.3Parametersandfractionalfactorsofgraphs
8.4Maximumandminimumfractional（g，f）-factors
8.5Connectedfractionalfactors
Index
References