Graph theory is a young but rapidly maturing subject. Even during the quarter of a century that I lectured on it in Cambridge, it changed considerably, and I have found that there is a clear need for a text which introduces the reader not only to the well-established results, but to many of the newer developments as well. It is hoped that this volume will go some way towards satisfying that need.

Apologia

Preface

I Fundamentals

I.1 Definitions

I.2 Paths， Cycles， and Trees

I.3 Hamilton Cycles and Euler Circuits

I.4 Planar Graphs

I.5 An Application of Euler Trails to Algebra

I.6 Exercises

II Electrical Networks

II.1 Graphs and Electrical Networks

II.2 Squaring the Square

II.3 Vector Spaces and Matrices Associated with Graphs

II.4 Exercises

II.5 Notes

III Flows， Connectivity and Matching

III.1 Flows in Directed Graphs

III.2 Connectivity and Menger‘s Theorem

III.3 Matching

III.4 Tutte‘s 1-Factor Theorem

……

Ⅳ Extremal Problems

Ⅴ Colouring

Ⅵ Ramsey Theory

Ⅶ Random Graphs

Ⅷ Graphs Groups and Matrices

Ⅸ Random Walks on Graphs

Ⅹ The Tutte Polynomial

Symbol Inedx

Name Index

Subject Index