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Graduate Texts in Mathematics
244
Editorial Board
S. Axler K.A. Ribet
Graduate Texts in Mathematics
1 TAKEUTI/ZARING. Introduction to Axiomatic
Set Theory. 2nd ed.
2 O
XTOBY. Measure and Category. 2nd ed.
3 S
CHAEFER. Topological Vector Spaces. 2nd ed.
4 H
ILTON/STAMMBACH. A Course in
Homological Algebra. 2nd ed.
5 M
AC LANE. Categories for the Working
Mathematician. 2nd ed.
6 H
UGHES/PIPER. Projective Planes.
7 J.-P. Serre. A Course in Arithmetic.
8 T
AKEUTI/ZARING. Axiomatic Set Theory.
9 H
UMPHREYS. Introduction to Lie Algebras and
Representation Theory.
10 C
OHEN. A Course in Simple Homotopy Theory.
11 C
ONWAY. Functions of One Complex
Variable I. 2nd ed.
12 B
EALS. Advanced Mathematical Analysis.
13 A
NDERSON/FULLER. Rings and Categories of
Modules. 2nd ed.
14 G
OLUBITSKY/GUILLEMIN. Stable Mappings
and Their Singularities.
15 B
ERBERIAN. Lectures in Functional Analysis
and Operator Theory.
16 W
INTER. The Structure of Fields.
17 R
OSENBLATT. Random Processes. 2nd ed.
18 H
ALMOS. Measure Theory.
19 H
ALMOS. A Hilbert Space Problem Book.
2nd ed.
20 H
USEMOLLER. Fibre Bundles. 3rd ed.
21 H
UMPHREYS. Linear Algebraic Groups.
22 B
ARNES/MACK. An Algebraic Introduction to
Mathematical Logic.
23 G
REUB. Linear Algebra. 4th ed.
24 H
OLMES. Geometric Functional Analysis and
Its Applications.
25 H
EWITT/STROMBERG. Real and Abstract
Analysis.
26 M
ANES. Algebraic Theories.
27 K
ELLEY. General Topology.
28 Z
ARISKI/SAMUEL. Commutative Algebra.
Vol. I.
29 Z
ARISKI/SAMUEL. Commutative Algebra.
Vol. II.
30 J
ACOBSON. Lectures in Abstract Algebra I.
Basic Concepts.
31 J
ACOBSON. Lectures in Abstract
Algebra II. Linear Algebra.
32 J
ACOBSON. Lectures in Abstract Algebra III.
Theory of Fields and Galois Theory.
33 H
IRSCH. Differential Topology.
34 S
PITZER. Principles of Random Walk. 2nd ed.
35 A
LEXANDER/WERMER. Several Complex
Variables and Banach Algebras. 3rd ed.
36 K
ELLEY/NAMIOKA et al. Linear Topological
Spaces.
37 M
ONK. Mathematical Logic.
38 G
RAUERT/FRITZSCHE. Several Complex
Variables.
39 A
RVESON. An Invitation to C-Algebras.
40 K
EMENY/SNELL/KNAPP. Denumerable Markov
Chains. 2nd ed.
41 A
POSTOL. Modular Functions and Dirichlet
Series in Number Theory. 2nd ed.
42 J.-P. S
ERRE. Linear Representations of Finite
Groups.
43 G
ILLMAN/JERISON. Rings of Continuous
Functions.
44 K
ENDIG. Elementary Algebraic Geometry.
45 L
O
`
Eve. Probability Theory I. 4th ed.
46 L
O
`
Eve. Probability Theory II. 4th ed.
47 M
OISE. Geometric Topology in Dimensions
2 and 3.
48 S
ACHS/WU. General Relativity for
Mathematicians.
49 G
RUENBERG/WEIR. Linear Geometry.
2nd ed.
50 E
DWARDS. Fermat’s Last Theorem.
51 K
LINGENBERG. A Course in Differential
Geometry.
52 H
ARTSHORNE. Algebraic Geometry.
53 M
ANIN. A Course in Mathematical Logic.
54 G
RAVER/WATKINS. Combinatorics with
Emphasis on the Theory of Graphs.
55 B
ROWN/PEARCY. Introduction to Operator
Theory I: Elements of Functional Analysis.
56 M
ASSEY. Algebraic Topology: An Introduction.
57 C
ROWELL/FOX. Introduction to Knot Theory.
58 K
OBLITZ. p-adic Numbers, p-adic Analysis,
and Zeta-Functions. 2nd ed.
59 L
ANG. Cyclotomic Fields.
60 A
RNOLD. Mathematical Methods in Classical
Mechanics. 2nd ed.
61 W
HITEHEAD. Elements of Homotopy Theory.
62 K
ARGAPOLOV/MERIZJAKOV. Fundamentals of
the Theory of Groups.
63 B
OLLOBAS. Graph Theory.
64 E
DWARDS. Fourier Series. Vol. I. 2nd ed.
65 W
ELLS. Differential Analysis on Complex
Manifolds. 2nd ed.
66 W
ATERHOUSE. Introduction to Affine Group
Schemes.
67 S
ERRE. Local Fields.
68 W
EIDMANN. Linear Operators in Hilbert
Spaces.
69 L
ANG. Cyclotomic Fields II.
70 M
ASSEY. Singular Homology Theory.
71 F
ARKAS/KRA. Riemann Surfaces. 2nd ed.
72 S
TILLWELL. Classical Topology and
Combinatorial Group Theory. 2nd ed.
73 H
UNGERFORD. Algebra.
74 D
AVENPORT. Multiplicative Number Theory.
3rd ed.
(continued after index)
J.A. Bondy U.S.R. Murty
Graph Theory
ABC
J.A. Bondy, PhD
Universit
´
e Claude-Bernard Lyon 1
Domaine de Gerland
50 Avenue Tony Garnier
69366 Lyon Cedex 07
France
Editorial Board
S. Axler
Mathematics Department
San Francisco State University
San Francisco, CA 94132
USA
U.S.R. Murty, PhD
Mathematics Faculty
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
K.A. Ribet
Mathematics Department
University of California, Berkeley
Berkeley, CA 94720-3840
USA
Graduate Texts in Mathematics series ISSN: 0072-5285
ISBN: 978-1-84628-969-9 e-ISBN: 978-1-84628-970-5
DOI: 10.1007/978-1-84628-970-5
Library of Congress Control Number: 2007940370
Mathematics Subject Classification (2000): 05C; 68R10
c
° J.A. Bondy & U.S.R. Murty 2008
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted
under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or trans-
mitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of
reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency.
Enquiries concerning reproduction outside those terms should be sent to the publishers.
The use of registered name, trademarks, etc. in this publication does not imply, even in the absence of a specific
statement, that such names are exempt from the relevant laws and regulations and therefore free for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the information
contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that
may be made.
Printed on acid-free paper
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springer.com
Dedication
To the memory of our dear friends and mentors
Claude Berge Paul Erd
˝
os Bill Tutte
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