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Graphs, Algorithms, and Optimization Discrete Mathematics and Its Applications Author: Kocay, William.; Kreher, Donald L cover Cover title: Graphs, Algorithms, and Optimization Discrete Mathematics and Its Applications author: Kocay, William.; Kreher, Donald L. publisher: CRC Press isbn10 | asin: 0203489055 print isbn13: 9780203620892 ebook isbn13: 9780203489055 language: English subject Graph algorithms. publication date: 2005 lcc: QA166.245.K63 2005eb ddc: 511/.5 subject: Graph algorithms. cover Page i DISCRETE MATHEMATICS AND ITS APPLICATIONS Series Editor KENNETH H.ROSEN GRAPHS, ALGORITHMS, AND OPTIMIZATION page_i Page ii DISCRETE MATHEMATICS AND ITS APPLICATIONS Series Editor Kenneth H.Rosen, Ph.D. Charles J.Colbourn and Jeffrey H.Dinitz, The CRC Handbook of Combinatorial Designs Charalambos A.Charalambides, Enumerative Combinatorics Steven Furino, Ying Miao, and Jianxing Yin, Frames and Resolvable Designs: Uses, Constructions, and Existence Randy Goldberg and Lance Riek, A Practical Handbook of Speech Coders Jacob E.Goodman and Joseph O’Rourke, Handbook of Discrete and Computational Geometry, Second Edition Jonathan Gross and Jay Yellen, Graph Theory and Its Applications Jonathan Gross and Jay Yellen, Handbook of Graph Theory Darrel R.Hankerson, Greg A.Harris, and Peter D.Johnson, Introduction to Information Theory and Data Compression, Second Edition Daryl D.Harms, Miroslav Kraetzl, Charles J.Colbourn, and John S.Devitt, Network Reliability: Experiments with a Symbolic Algebra Environment David M.Jackson and Terry I.Visentin, An Atlas of Smaller Maps in Orientable and Nonorientable Surfaces Richard E.Klima, Ernest Stitzinger, and Neil P.Sigmon, Abstract Algebra Applications with Maple Patrick Knupp and Kambiz Salari, Verification of Computer Codes in Computational Science and Engineering Donald L.Kreher and Douglas R.Stinson, Combinatorial Algorithms: Generation Enumeration and Search file:///G|/SMILEY/0203489055__gigle.ws/0203489055/files/__joined.html[01/10/2009 15:18:30] cover Charles C.Lindner and Christopher A.Rodgers, Design Theory Alfred J.Menezes, Paul C.van Oorschot, and Scott A.Vanstone, Handbook of Applied Cryptography Richard A.Mollin, Algebraic Number Theory Richard A.Mollin, Fundamental Number Theory with Applications Richard A.Mollin, An Introduction to Cryptography Richard A.Mollin, Quadratics page_ii Page iii Continued Titles Richard A.Mollin, RSA and Public-Key Cryptography Kenneth H.Rosen, Handbook of Discrete and Combinatorial Mathematics Douglas R.Shier and K.T.Wallenius, Applied Mathematical Modeling: A Multidisciplinary Approach Douglas R.Stinson, Cryptography: Theory and Practice, Second Edition Roberto Togneri and Christopher J.deSilva, Fundamentals of Information Theory and Coding Design Lawrence C.Washington, Elliptic Curves: Number Theory and Cryptography Kun-Mao Chao and Bang Ye Wu, Spanning Trees and Optimization Problems Juergen Bierbrauer, Introduction to Coding Theory William Kocay and Donald L.Kreher, Graphs, Algorithms, and Optimization page_iii Page iv This page intentionally left blank. page_iv Page v DISCRETE MATHEMATICS AND ITS APPLICATIONS Series Editor KENNETH H.ROSEN GRAPHS, ALGORITHMS, AND OPTIMIZATION WILLIAM KOCAY DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF MANITOBA DONALD L.KREHER DEPARTMENT OF MATHEMATICAL SCIENCES MICHIGAN TECHNOLOGICAL UNIVERSITY CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London NewYork Washington, D.C. page_v Page vi This edition published in the Taylor & Francis e-Library, 2005. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. Library of Congress Cataloging-in-Publication Data Kocay, William. Graphs, algorithms, and optimization/William Kocay, Donald L.Kreher. p. cm.—(Discrete mathematics and its applications) Includes bibliographical references and index. ISBN 1-58488-396-0 (alk. paper) 1. Graph algorithms. I. Kreher, Donald L. II. Title. III. Series. QA166.245.K63 2004 511′.5–dc22 2004056153 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable file:///G|/SMILEY/0203489055__gigle.ws/0203489055/files/__joined.html[01/10/2009 15:18:30] cover efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press for such copying. Direct all inquiries to CRC Press, 2000 N.W.Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. Visit the CRC Press Web site at www.crcpress.com © 2005 by Chapman & Hall/CRC Press No claim to original U.S. Government works ISBN 0-203-48905-5 Master e-book ISBN ISBN 0-203-62089-5 (OEB Format) International Standard Book Number 1-58488-396-0 (Print Edition) Library of Congress Card Number 2004056153 page_vi Page vii The authors would like to take this opportunity to express their appreciation and gratitude to the following people who have had a very significant effect on their mathematical development: Adrian Bondy, Earl Kramer, Spyros Magliveras, Ron Read, and Ralph Stanton. This book is dedicated to the memory of William T.Tutte, (1917–2002) “the greatest of the graphmen” page_vii Page viii This page intentionally left blank. page_viii Page ix Preface Our objective in writing this book is to present the theory of graphs from an algorithmic viewpoint. We present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs. Graph theory is a rich source of problems and techniques for programming and data structure development, as well as 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 is any major programming language (e.g., C, C++, Java). The algorithms are presented in a generic style and are not dependent on any particular programming 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 available. A possible first course would consist of Chapters 1, 2, 3, 4, 6, 8, 9, 10, 11, and 12, and a first course stressing optimization would consist of Chapters 1, 2, 3, 4, 8, 9, 10, 14, 15, and 16. Experience indicates that the students consider these substantial courses. One or two chapters could be omitted for a lighter course. We would like to thank the many people who provided encouragement while we wrote this book, pointed out typos and errors, and gave useful suggestions. In particular, we would like to convey our thanks to Ben Li and John van Rees of the University of Manitoba for proofreading some chapters. William Kocay Donald L.Kreher page_ix Page x file:///G|/SMILEY/0203489055__gigle.ws/0203489055/files/__joined.html[01/10/2009 15:18:30] cover This page intentionally left blank. page_x Page xi William Kocay obtained his Ph.D. in Combinatorics and Optimization from the University of Waterloo in 1979. He is currently a member of the Computer Science Department, and an adjunct member of the Mathematics Department, at the University of Manitoba, and a member of St. Paul’s College, a college affiliated with the University of Manitoba. He has published numerous research papers, mostly in graph theory and algorithms for graphs. He was managing editor of the mathematics journal Ars Combinatoria from 1988 to 1997. He is currently on the editorial board of that journal. He has had extensive experience developing software for graph theory and related mathematical structures. Donald L.Kreher obtained his Ph.D. from the University of Nebraska in 1984. He has held academic positions at Rochester Institute of Technology and the University of Wyoming. He is currently a University Professor of Mathematical Sciences at Michigan Technological University, where he teaches and conducts research in combinatorics and combinatorial algorithms. He has published numerous research papers and is a co-author of the internationally acclaimed text “Combinatorial Algorithms: Generation Enumeration and Search”, CRC Press, 1999. He serves on the editorial boards of two journals. Professor Kreher is the sole recipient of the 1995 Marshall Hall Medal, awarded by the Institute of Combinatorics and its Applications. page_xi Page xii This page intentionally left blank.
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