Color-Induced Graph Colorings
A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge colorin
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Ping Zhang
Color-Induced Graph Colorings
123
SpringerBriefs in Mathematics
Series Editors Nicola Bellomo Michele Benzi Palle E.T. Jorgensen Tatsien Li Roderick Melnik Otmar Scherzer Benjamin Steinberg Lothar Reichel Yuri Tschinkel G. George Yin Ping Zhang
SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians. More information about this series at http://www.springer.com/series/10030
Ping Zhang
Color-Induced Graph Colorings
123
Ping Zhang Department of Mathematics Western Michigan University Kalamazoo, MI, USA
ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-3-319-20393-5 ISBN 978-3-319-20394-2 (eBook) DOI 10.1007/978-3-319-20394-2 Library of Congress Control Number: 2015942698 Mathematics Subject Classification (2010): 05C15, 05C70, 05C78 Springer Cham Heidelberg New York Dordrecht London © Ping Zhang 2015 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
Preface
The interest in edge colorings of graphs can be traced back to 1880 when the Scottish mathematician Peter Guthrie Tait attempted to solve the Four Color Problem with the aid of edge colorings. Despite the fact that Tait’s approach was not successful, it initiated a new concept. In 1964, Vadim Vizing proved that the minimum number of colors needed to color the edges of a graph so that every two adjacent edges are colored differently (proper edge colorings) is one of two numbers, namely either the maximum degree or the maximum degree plus one. This result led to an increased interest and study of edge colorings in grap
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