Colorings
This chapter looks at a subject occurring quite often in graph theory: colorings. We shall prove the two fundamental major results in this area, namely the theorem of Brooks on vertex colorings and the theorem of Vizing on edge colorings. As an aside, we
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For further volumes: http://www.springer.com/series/3339
Dieter Jungnickel
Graphs, Networks and Algorithms Fourth Edition
Dieter Jungnickel Institut f¨ur Mathematik Universit¨at Augsburg Augsburg Germany
ISSN 1431-1550 Algorithms and Computation in Mathematics ISBN 978-3-642-32277-8 ISBN 978-3-642-32278-5 (eBook) DOI 10.1007/978-3-642-32278-5 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012951158 Mathematics Subject Classification: 11-01, 11Y40, 11E12, 11R29 © Springer-Verlag Berlin Heidelberg 1998, 2004, 2008, 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. G.H. Hardy
To my teacher, Prof. Hanfried Lenz
Preface to the Fourth Edition
Welcome back, my friends, to the show that never ends.... Emerson, Lake & Palmer
Once again, the new edition has been thoroughly revised, even though the changes are less extensive than for the third edition. (Well, one does hope for some sort of convergence of the writing process.) In particular, I have again added some further material: more on NPcompleteness (especially on dominating sets), a section on the GallaiEdmonds structur
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