Total Colourings of Graphs
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, togeth
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H. P. Yap
Total Colourings of Graphs
Author Hian-Poh Yap National University of Singapore Department of Mathematics Lower Kent Ridge Road Singapore 0511, Republic of Singapore
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Yap, Hian Poh: Total colourings of graphs / Hian Poh Yap. - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Tokyo: Springer, 1996 (Lecture notes in mathematics; 1623) ISBN 3-540-60717-X
NE:GT
CatE: Mathematics Subject Classification (1991): 05C15, 05C35, 05C75 ISBN 3-540-60717-X Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions ofthe German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1996 Printed in Germany Typesetting: Camera-ready TEX output by the author SPIN: 10479714 46/3142-543210 - Printed on acid-free paper
Preface I started writing this book in 1990 and completed the first draft in October 1991. It then took me another one and a half years (J une 1992 to December 1993) to revise
the first draft. My objective in writing this book is to give an up-to-date account of total colourings of graphs which can be used as a graph theory course/seminar materials for advanced undergraduate and graduate students and as a reference for researchers. To achieve the objectives, easy-to-read, detailed proofs of almost all of the theorems presented in this book, and numerous examples and exercises are provided here. Many open problems are also mentioned. I hope that through this rapid introduction I shall be able to bring the readers to the frontier of this currently very active field in graph theory. After the first draft of this manuscript was completed, I used it as lecturing material in my graph theory course offered to the advanced undergraduate students of the National University of Singapore (NUS). I thank my students for their patience in attending my lectures and for giving me their valuable feedback. I would like to thank the NUS for granting me a lO-month (1 July 1991 to 30 April 1992) sabbatical leave so that I could concentrate on writing and revising the manuscript. I would also like to thank the NUS for granting me conference leaves (June 1993 and June 1995) and to the Japan Society for the Promotion of Science for sponsoring my visit to three universities in Japan (12 April to May 1, 1993) so that I could have direct discussions w
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