Map Color Theorem
In 1890 P. J. Heawood [35] published a formula which he called the Map Colour Theorem. But he forgot to prove it. Therefore the world of mathematicians called it the Heawood Conjecture. In 1968 the formula was proven and therefore again called the Map Col
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H erausgegeben von S. S. Chern J. L. Doob J. Douglas, jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf W. Maak S. MacLane W. Magnus M. M. Postnikov F. K. Schmidt D. S. Scott K. Stein Geschiiftsfuhrende H erausgeber B. Eckmann J. K. Moser B. L. van der Waerden
Gerhard Ringel
Map Color Theorem
With 176 Figures
Springer-Verlag New York Heidelberg Berlin 1974
Gerhard Ringel University of California, Santa Cruz, California 95064, U.S.A.
Geschaftsfiihrende Herausgeber B.Eckmann Eidgenossische Technische Hochschule Zurich J. K. Moser Courant Institute of Mathematical Sciences, New York B. L. van der Waerden Mathematisches Institut der U niversitat ZUrich
AMS Subject Classifications (1970): 05ClO, 05C15, 55A15
ISBN-13: 978-3-642-65761-0 DOl: 10.1007/978-3-642-65759-7
e-ISBN-13: 978-3-642-65759-7
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, fe-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1974. Library of Congress Catalog Card Number 73-17986. Softcover reprint of the hardcover 1st edition 1974
Dedicated to Professor and Mrs. 1. W. T. Youngs
Foreword
In 1890 P. J. Heawood [35] published a formula which he called the Map Colour Theorem. But he forgot to prove it. Therefore the world of mathematicians called it the Heawood Conjecture. In 1968 the formula was proven and therefore again called the Map Color Theorem. (This book is written in California, thus in American English.) Beautiful combinatorial methods were developed in order to prove the formula. The proof is divided into twelve cases. In 1966 there were three of them still unsolved. In the academic year 1967/68 J. W. T. Youngs invited me to work with him on those three cases at Santa Cruz. Surprisingly our joint effort led to the solution of all three cases. It was a year of hard work but great pleasure. Working together was extremely profitable and enjoyable. In spite of the fact that we saw each other every day, Ted wrote a letter to me, which I present here in shortened form: Santa Cruz, March 1, 1968 Dear Gerhard: Last night while I was checking our results on Cases 2, 8 and 11, and thinking of the great pleasure we had in the afternoon with the extraordinarily elegant new solution for Case 11, it seemed to me appropriate to pause for a few minutes and dictate a historical memorandum. We began working on Case 8 on 10 October 1967, and it was settled on Tuesday night, 14 November 1967. You had a crucial idea in regard to additional adjacencies on 29 October, but I could not finish the regular part of the problem with your program. On Monday afternoon, 30 October, we sat down at my desk at about 4: 30 p.m. and you developed a seco
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