✦ LIBER ✦

A New Bound on the Cyclic Chromatic Number

✍ Scribed by Daniel P. Sanders; Yue Zhao

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 116 KB
Volume: 83
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2046

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✦ Synopsis

In 1969, Ore and Plummer defined an angular coloring as a natural extension of the Four Color Problem: a face coloring of a plane graph where faces meeting even at a vertex must have distinct colors. A natural lower bound is the maximum degree 2 of the graph. Some graphs require w 3 2 2x colors in an angular coloring. Ore and Plummer gave an upper bound of 22, which was improved to w 9 5 2x by the authors with Borodin. This article gives a new upper bound of W 5 9 2X on the angular chromatic number. The cyclic chromatic number is the equivalent dual vertex coloring problem.

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