Skip to main content
SpringerLink
Log in
Book cover

Map Color Theorem

  • Book
  • © 1974

Overview

Authors:
  1. Gerhard Ringel

    1. University of California, Santa Cruz, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (12 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. Problems, Illustrations, History

    • Gerhard Ringel
    Pages 1-9

  3. Graph Theory

    • Gerhard Ringel
    Pages 10-33

  4. Classification of Surfaces

    • Gerhard Ringel
    Pages 34-53

  5. Graphs on Surfaces

    • Gerhard Ringel
    Pages 54-73

  6. Combinatorics of Embeddings

    • Gerhard Ringel
    Pages 74-88

  7. Orientable Cases 1, 4, and 9

    • Gerhard Ringel
    Pages 89-101

  8. Orientable Cases 11, 2, and 8

    • Gerhard Ringel
    Pages 102-129

  9. Non-Orientable Cases (Index 1)

    • Gerhard Ringel
    Pages 130-145

  10. Solutions of Index 2 and 3

    • Gerhard Ringel
    Pages 146-158

  11. Construction by Induction

    • Gerhard Ringel
    Pages 159-168

  12. Orientable Case 0

    • Gerhard Ringel
    Pages 169-177

  13. Related Problems

    • Gerhard Ringel
    Pages 178-183

  14. Back Matter

    Pages 184-194
    Download chapter PDF
Back to top

Keywords

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.

Authors and Affiliations

  • University of California, Santa Cruz, USA

    Gerhard Ringel

Bibliographic Information

  • Book Title: Map Color Theorem

  • Authors: Gerhard Ringel

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-65759-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1974

  • Softcover ISBN: 978-3-642-65761-0Published: 07 December 2011

  • eBook ISBN: 978-3-642-65759-7Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 194

  • Topics: Topology

Publish with us

Policies and ethics

Back to top

Search

Navigation