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June 1, 1976Illinois Journal of Mathematics31 citationsOpen Access

The existence of unavoidable sets of geographically good configurations

KAK. I. AppelWHWolfgang Haken

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Abstract

A set of configurations is unavoidable if every planar map contains at least one element of the set. A configuration L is called geographically good if whenever a member country M of L has any three neighbors N₁, N₂, N₃ which are not members of L then N₁, N₂, N₃ 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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Cite This Study

Appel et al. (1976) studied this question.

synapsesocial.com/papers/6a2204083081c2f8f8e22e92https://doi.org/10.1215/ijm/1256049898
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