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On the edge-coloring problem for a class of 4-regular maps

✍ Scribed by F. Jaeger; H. Shank

Publisher: John Wiley and Sons
Year: 1981
Tongue: English
Weight: 300 KB
Volume: 5
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190050308

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✦ Synopsis

Abstract

A (plane) 4‐regular map G is called C‐simple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case σ (G) is the smallest integer k such that the curves of G can be colored with k colors in such a way that no two curves of the same color intersect. We prove that if σ (G) ≤ 4, G is edge colorable with 4 colors. Moreover we show that a similar result for maps G with σ(G) ≤ 5 would imply the Four‐Color Theorem.

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