Graphs, Algorithms, and Optimization

504 Pages·2017·18.095 MB·English

by  Kocay, William, Kreher, Donald L

DISCRETE MATHEMATICS AND ITS APPLICATIONS
Series Editor KENNETH H. ROSEN
GRAPHS,
ALGORITHMS,
OPTIMIZATION
AND
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SCITAMEHTAM
STI SNOITACILPPA
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Jonathan Gross and Jay Yellen, hparG yroehT dna stI snoitacilppA
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ETERCSID SCITAMEHTAM DNA STI SNOITACILPPA
Series Editor HTENNEK .H NESOR
,SHPARG
,SMHTIROGLA
NOITAZIMITPO
DNA
WILLIAM YACOK
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSI1Y OF MANITOBA
.L
DONALD KREHER
DEPARTMENT OF MATHEMATICAL SCIENCES
MICHIGAN TECHNOLOGICAL UNIVERSI1Y
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NAMPAHC & CRCULAH
A CRC Press Company
acoB notaR nodnoL New kroY Washington, .C.D
'fransferred to Digital Printing 2005
Library of Congress Cataloging-in-Publication Data
,yacoK William.
Graphs, algorithms, and optimization I William ,yacoK Donald L. .reherK
.p .me - (Discrete mathematics and sti applications)
Includes bibliographical references and .xedni
ISBN 1-58488-396-0 .kla( paper)
l. Graph algorithms. I. ,reherK Donald .L .II .eltiT ill. .seireS
QA166.245.K63 2004
115 '.5---dc22 2004056153
This book contains information obtained from authentic and highly regarded .secruos Reprinted material
si quoted with permission, and sources era indicated. A wide variety of references era .detsil Reasonable
efforts evah been made ot publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of lla materials or rof eht consequences of their .esu
Neither this book nor any part may be reproduced or transmitted in yna form or by yna means, electronic
or mechanical, including photocopying, microfilming, and recording, or by yna information storage or
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No claim to original .S.U Government works
International Standard Book Number 1-58488-396-0
Library of Congress Card Number 2004056153
The authors would like ot take siht opportunity ot express their appreciation and
gratitude ot the following people who evah had a very significant effect on their
mathematical development:
Adrian Bondy, Earl Kramer, Spyros Magliveras, Ron Read, and Ralph Stanton.
This book si dedicated ot the memory of
William .T Tutte, (1917-2002)
" the greatest of the graphmen "

Preface
Our objective in writing siht book is ot present eht theory of graphs from na algo
rithmic viewpoint. eW present the graph theory in a rigorous, but informal style
and cover most of the main areas of graph .yroeht The ideas of surface topology
are presented from na intuitive point of .weiv eW evah osla included a discussion
on linear programming that emphasizes problems in graph .yroeht The text si
suitable for students in computer science or mathematics programs.
Graph theory si a rich source of problems and techniques for programming
and data structure development, sa well sa for the theory of computing, including
NP-completeness and polynomial reduction.
This book could be used a textbook for a third or fourth year course on graph
algorithms which contains a programming content, or for a more advanced course
at the fourth year or graduate .level It could be used in a course in which the
programming language si any major programming language ,.g.e( ,C C++, .)avaJ
The algorithms are presented in a generic style and are not dependent on yna
particuplraorg ramming language.
The text could also be used for a sequence of courses like "Graph Algorithms
I" and "Graph Algorithms II". The courses offered would depend on the selection
of chapters included. A typical course will begin with Chapters ,1 ,2 3, and .4 At
this point, a number of options are .elbaliava
A possible tsrif course would consist of Chapters ,1 ,2 ,3 ,4 ,6 ,8 ,9 ,01 ,11 and
21 , and a tsrif course stressing optimization would consist of Chapters ,1 ,2 ,3
4, ,8 ,9 ,01 ,41 ,51 and .61 Experience indicates that the students consider these
substantial courses. One or two chapters could be omitted for a lighter course.
eW would like ot thank the many people ohw provided encouragement while
we wrote this book, pointed out typos and errors, and gave useful suggestions. nI
particular, we would like ot convey our thanks ot Ben Li and John nav Rees of the
University of Manitoba for proofreading some chapters.
William Kocay
Donald L. Kreher