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Every Planar Map is Four Colorable
Kenneth Appel and Wolfgang Haken
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Contemporary Mathematics
1989; 741 pp; softcover
Volume: 98
Reprint/Revision History:
reprinted with corrections 1992
ISBN-10: 0-8218-5103-9
ISBN-13: 978-0-8218-5103-6
List Price: US$114
Member Price: US$91.20
Order Code: CONM/98
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In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.

Table of Contents

Introduction
  • History
  • C- and D-Reducibility
  • Unavoidable Sets and our Discharging Procedure
  • Details of the Proof
  • Our Checking Procedure
Part I: Discharging
  • Introduction
  • The Discharging Procedure
  • The Set \(\cal U\) of Reducible Configurations
  • Probabilistic Considerations
  • Possible Improvements
Part II: Reducibility
  • Introduction
  • The Computer Programs
  • Immersion Reducibility
  • The Unavoidable Set \(\cal U\) of Reducible Configurations
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