现代图论：英文本

Apologia
Preface
Fundamentals
I.1Definitions
I.2Paths,Cycles,andTrees
I.3HamiltonCyclesandEulerCircuits
I.4PlanarGraphs
I.5AnApplicationofEulerTrailstoAlgebra
I.6Exercises
IIElectricalNetworks
II.1GraphsandElectricalNetworks
II.2SquaringtheSquare
II.3VectorSpacesandMatricesAssociatedwithGraphs
II.4Exercises
II.5Notes
IIIFlows,ConnectivityandMatching
III.1FlowsinDirectedGraphs
II1.2ConnectivityandMenger'sTheorem
III.3Matching
III.4Tutte's1-FactorTheorem
III.5StableMatchings
III.6Exercises
III.7Notes
IVExtremalProblems
IV.1PathsandCycles
IV.2CompleteSubgraphs
IV.3HamiltonPathsandCycles
IV.4TheStructureofGraphs
IV.5Szemeredi'sRegularityLemma
IV.6SimpleApplicationsofSzemeredi'sLemma
IV.7Exercises
IV.8Notes
VColouring
V.1VertexColouring
V.2EdgeColouring
V.3GraphsonSurfaces
V.4ListColouring
V.5PerfectGraphs
V.6Exercises
V.7Notes
VIRamseyTheory
VI.1TheFundamentalRamseyTheorems
VI.2CanonicalRamseyTheorems
VI.3RamseyTheoryForGraphs
VI.4RamseyTheoryforIntegers
VI.5Subsequences
VI.6Exercises
VI.7Notes
VIIRandomGraphs
VII.1TheBasicModels--TheUseoftheExpectation
VII.2SimplePropertiesofAlmostAllGraphs
VII.3AlmostDeterminedVariablesTheUseoftheVariance
VII.4HamiltonCycles--TheUseofGraphTheoreticTools
VII.5ThePhaseTransition
VII.6Exercises
VII.7Notes
VIIIGraphs,GroupsandMatrices
VIII.1CayleyandSchreierDiagrams
VIII.2TheAdjacencyMatrixandtheLaplacian
VIII.3StronglyRegularGraphs