editor's statement

foreword

introduction

chapter i graphs and subgraphs

i.1 definitions

1.2 isomorphism

1.3 subgraphs

1.4 vertices of attachment

1.5 components and connection

1.6 deletion of an edge

1.7 lists of nonisomorphic connected graphs

1.8 bridges

1.9 notes

exercises

references

chapter ii contractions and the theorem of menger

ii.1 contractions

ii.2 contraction of an edge

ii.3 vertices of attachment

ii.4 separation numbers

.ii.5 menger's theorem

ii.6 hall's theorem

ii.7 notes

exercises

references

chapter iii 2-connection

iii.1 separable and 2-connected graphs

iii.2 constructions for 2-connected graphs

iii.3 blocks

iii.4 arms

iii.5 deletion and contraction of an edge

ii1.6 notes

exercises

references

chapter iv 3-connection

iv.1 multiple connection

iv.2 some constructions for 3-connected graphs

iv.3 3-blocks

iv.4 cleavages

iv.5 deletions and contractions of edges

iv.6 the wheel theorem

iv.7 notes

exercises

references

chapter v reconstruction

v.i the reconstruction problem

v.2 theory and practice

v.3 kelly's lemma

v.4 edge-reconstruction

v.5 notes

exercises

references

chapter vi digraphs and paths

vi.1 digraphs

vi.2 paths

vi.3 the best theorem

vi.4 the matrix-tree theorem

vi.5 the laws of kirchhoff

vi.6 identification of vertices

vi.7 transportation theory

vi.8 notes

exercises

references

chapter vii alternating paths

vii.1 cursality

vii.2 the bicursal subgraph

vii.3 bicursal units

vii.4 alternating barriers

vii.5 f-factors and f-barriers

vii.6 the f-factor theorem

vii.7 subgraphs of minimum deficiency

vii.8 the bipartite case

vii.9 a theorem of erdos and gallai

vii.10 notes

exercises

references

chapter viii algebraic duality

viii.i chain-groups

viii.2 primitive chains

viii.3 regular chain-groups

viii.4 cycles

viii.5 coboundaries

viii.6 reductions and contractions

viii.7 algebraic duality

viii.8 connectivity

viii.9 on transportation theory

viii.10 incidence matrices

viii.11 matroids

viii.12 notes

exercises

references

chapter ix polynomials associated with graphs

ix.1 v-functions

ix.2 the chromatic polynomial

ix.3 colorings of graphs

ix.4 the flow polynomial

ix.5 tait colorings

ix.6 the dichromate of a graph

ix.7 some remarks on reconstruction

ix.8 notes

exercises

references

chapter x combinatorial maps

x.1 definitions and preliminary theorems

x.2 orientability

x.3 duality

x.4 isomorphism

x.5 drawings of maps

x.6 angles

x.7 operations on maps

x.8 combinatorial surfaces

x.9 cycles and coboundaries

x. 10 notes

exercises

references

chapter xi planarity

xi.1 planar graphs

xi.2 spanning subgraphs

xi.3 jordan's theorem

xi.4 connectivity in planar maps

xi.5 the cross-cut theorem

xi.6 bridges

xi.7 an algorithm for planarity

xi.8 peripheral circuits in 3-connected graphs

xi.9 kuratowski's theorem

xi.10 notes

exercises

references

index