Preface to the fourth edition
1 Introduction
1 What is a graph?
2 Definitions and examples
2 Definition
3 Examples
4 Three puzzles
3 Paths and cycles
5 Connectivity
6 Eulerian graphs
7 Hamiltonian graphs
8 Some algorithms
4 Trees
9 Properties of trees
10 Counting trees
11 More applications
5 Planarity
12 Planar graphs
13 Eulers formula
14 Graphs on other surfaces
15 Dual graphs
16 infinite graphs
6 Colouring graphs
17 Colouring vertices
18 Brooks theorem
19 Colouring maps
20 Colouring edges
21 Chromatic polynomials
7 Digraphs
22 Definitions
23 Eulerian digraphs and tournaments
24 Markov chains
8 Matching， marriage and Mengers theorem
25 Halls marriage theorem
26 Transversal theory
27 Applications of Halls theorem
28 Mengers theorem
29 Network flows
9 Matroids
30 Introduction to matroids
31 Examples of matroids
32 Matroids and graphs
33 Matroids and transversals
Appendix
Bibliography
Solutions to selected exercises
Index of symbols
Index of definitions
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