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Introduction to Graph Theory
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Introduction to Graph Theory Introduction to Graph Theory
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Introduction to Graph Theory
Fourth edition
Introduction to
Graph Theory
Fourth edition
Robin J. Wilson
Addison Wesley Longman Limited
Edinburgh Gate, Harlow,
Essex CM20 2JE, England
and Associated Companies throughout the
world.
©Robin Wilson 1972, 1996
All rights reserved; no part of this publication may be reproduced, stored in any retrieval system, or
transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise
without either the prior written permission of the Publishers or a licence permitting restricted copying in
the United Kingdom issued by the Copyright Licensing Agency Ltd., 90 Tottenham Court Road, London
W1P9HE.
First published by Oliver & Boyd, 1972
Second edition published by Longman Group Ltd, 1979
Third edition, 1985
Fourth edition, 1996
Reprinted 1998
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0-582-24993-7
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
Set by 8 in 10 on 12pt Times
Produced through Longman Malaysia, PP
Contents
Preface to the fourth edition vii
1 Introduction
1 What is a graph? 1
2 Definitions and examples
2 Definition 8
3 Examples 17
4 Three puzzles 21
3 Paths and cycles
5 Connectivity 26
6 Eulerian graphs 31
7 Hamiltonian graphs 35
8 Some algorithms 38
4 Trees
9 Properties of trees 43
10 Counting trees 47
11 More applications 51
5 Planarity
12 Planar graphs
13 Euler's formula 60
14 Graphs on other surfaces 70
15 Dual graphs 73
16 Infinite graphs 77
6 Colouring graphs
17 Colouring vertices 81
18 Brooks' theorem 86
19 Colouring maps 88
20 Colouring edges 92
21 Chromatic polynomials 96
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