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June 1976 The existence of unavoidable sets of geographically good configurations
K. Appel, W. Haken
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Illinois J. Math. 20(2): 218-297 (June 1976). DOI: 10.1215/ijm/1256049898

Abstract

A set of configurations is unavoidable if every planar map contains at least one element of the set. A configuration $\mathcal{L}$ is called geographically good if whenever a member country $M$ of $\mathcal{L}$ has any three neighbors $N_{1}$, $N_{2}$, $N_{3}$ which are not members of $\mathcal{L}$ then $N_{1}$, $N_{2}$, $N_{3}$ are consecutive (in some order) about $M$.

The main result is a constructive proof that there exist finite unavoidable sets of geographically good configurations. This result is the first step in an investigation of an approach towards the Four Color Conjecture.

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K. Appel. W. Haken. "The existence of unavoidable sets of geographically good configurations." Illinois J. Math. 20 (2) 218 - 297, June 1976. https://doi.org/10.1215/ijm/1256049898

Information

Published: June 1976
First available in Project Euclid: 20 October 2009

zbMATH: 0322.05141
MathSciNet: MR0392641
Digital Object Identifier: 10.1215/ijm/1256049898

Subjects:
Primary: 05C15
Secondary: 57C35

Rights: Copyright © 1976 University of Illinois at Urbana-Champaign

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Vol.20 • No. 2 • June 1976
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