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GRAPHTHEORY
WITHAPPLICATIONS
J.A.BondyandU.S.R.Murty
UniversityofWaterloo,
Ontario,Canada'
NORfH-HOLLAND
NewYork•Amsterdam•Oxford
®J.A.BondyandV.S.R.Muny1976
FirstpublishedinGreatBritain1976by
The·MacmillanPressLtd.
FirstpublishedintheU.S.A.1976by
ElseyierSciencePublishingCo.,Inc.
52VanderbiltAvenue,NewYork,N.Y10017
FifthPrinting,1982.
SoleDistributor
intheU.S.A:ElsevierSciencePublishingCo.
.,Inc.Library
ofCongressCataloginginPublicationDataBondy,JohnAdrian.
Graphtheorywith,applications.
Bibliography:p.
Includes
index.QA166.B671979511'.575-29826·
ISBN7 All formorbyanymeans,withoutpermission.Printed
intheUnitedStatesofAmerica·Toourparents
Preface
variety 'applications' gorithms shouldallbeattempted. arelisted. helpful appendixV. Many usChungphaisan
Preface
vii manuscriptandvaluablesuggestions, andtotheubiquitousG.O.M.forhis kindness andconstantencouragement. B. financialsupport.Finally,wewouldlike toexpressourappreciationtoJoanSelwoodfor
artwork..J.A.Bondy
U.S.R.Murty
Contents
Preface
1GRAPHSANDSUBGRAPHS
1.1GraphsandSimpleGraphs.
1.2GraphIsomorphism
1.3TheIncidenceandAdjacencyMatrices
1.4Subgraphs
1.5VertexDegrees_
1.6Pathsan"dConnection
1.7Cycles._
Applications
1.8The"ShortestPathProblem_
1.,9Sperner'sLemma.
2TREES
2.1Trees
2.2CutEdgesandBonds..
2.3CutV'ertices.
2.4Cayley'sFormula.
Applications.
2.5TheCo"nnectorProblem
3CONNECTIVITY
3.1Connectivity.
3.2Block"s"_
4EULERTOURSAN-nHAMILTONCYCLES"
4.1EulerTours_
4.2HamiltonCycles.
Applications
4.3The",ChinesePostmanProblem
4.4TheTravellin,g'SalesDlanProblem
vi 1 4 7 8 10 12 14 15 2125
27
31
32
,36" ' 42'
44.
47
51
53
62
65
Contents
5MATCHINGS
5.1Matchings
5.2MatchingsandCoveringsinBipartiteGraphs
5.3PerfectMatchings.
Applications
5.4ThePersonnelAssignmentProblem'.
5.5TheOptimalAssignmentProblem
. 6EDGECOLOURINGS6.1EdgeChromaticNumber
6.2Vizing'sTheorem.
Applications
TheTimetablingProblem
7INDEPENDENTSETSANDCLIQUES
7.1IndependentSets.
7.2Ramsey's
7.3Turan'sTheorem.
Applications
7.4Schur'sTheorem.
7.5AGeometryProblem.
8VERTEXCOLOU'RINGS
8.1ChromaticNumber
8.2Brooks'Theorem.
8.3Haj6s'·.
8..4Chromatic
8.5GirthandChromaticNumber
Applications
8.6AStorageProblem
9PLANARGRAPHS
IX 7072
76
80
86
91
93
96
·101
·103,
109·112
·113
·117
·122
123125
129
.131