© 1974

Map Color Theorem


Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 209)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Gerhard Ringel
    Pages 1-9
  3. Gerhard Ringel
    Pages 10-33
  4. Gerhard Ringel
    Pages 34-53
  5. Gerhard Ringel
    Pages 54-73
  6. Gerhard Ringel
    Pages 74-88
  7. Gerhard Ringel
    Pages 89-101
  8. Gerhard Ringel
    Pages 102-129
  9. Gerhard Ringel
    Pages 130-145
  10. Gerhard Ringel
    Pages 146-158
  11. Gerhard Ringel
    Pages 159-168
  12. Gerhard Ringel
    Pages 169-177
  13. Gerhard Ringel
    Pages 178-183
  14. Back Matter
    Pages 184-194

About this book


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 on those three cases at Santa Cruz. Sur­ invited me to work with him prisingly 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 extra­ ordinarily 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.


Mehrfarbenproblem boundary element method form proof theorem topology

Authors and affiliations

  1. 1.University of CaliforniaSanta CruzUSA

Bibliographic information

  • Book Title Map Color Theorem
  • Authors G. Ringel
  • Series Title Die Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1974
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-06548-7
  • Softcover ISBN 978-3-642-65761-0
  • eBook ISBN 978-3-642-65759-7
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XII, 194
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topology
  • Buy this book on publisher's site