A Kaleidoscopic View of Graph Colorings
This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings,
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Ping Zhang
A Kaleidoscopic View of 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
A Kaleidoscopic View of 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 978-3-319-30516-5 ISBN 978-3-319-30518-9 (eBook) DOI 10.1007/978-3-319-30518-9 Library of Congress Control Number: 2016934706 Mathematics Subject Classification (2010): 05C15, 05C70, 05C78, 05C90 © The Author 2016 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 This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface
It is the origin of the Four Color Problem by Francis Guthrie in 1852 that led to coloring maps and then to coloring planar graphs—not only coloring its regions but coloring its vertices and edges as well. In 1880, when Peter Guthrie Tait attempted to solve the Four Color Problem, it was known that the Four Color Problem could be solved for all planar graphs if it could be solved for all 3-regular bridgeless planar graphs. Tait was successful in showing that the Four Color Problem could be solved in the affirmative if it could be shown that the edges of every 3-regular bridgeless planar graph could be colored with three col
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