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Ond-diagonal colorings

✍ Scribed by Sanders, Daniel P.; Zhao, Yue

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 599 KB
Volume: 22
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199606)22:2<155::aid-jgt6>3.0.co;2-m

No coin nor oath required. For personal study only.

✦ Synopsis

A coloring of a graph embedded on a surface is d-diagonal if any pair of vertices that are in the same face after the deletion of a t most d edges of the graph must be colored differently. Hornak and Jendrol introduced d-diagonal colorings as a generalization of cyclic colorings and diagonal colorings. This paper proves a conjecture of Hornak and Jendrol that plane quadrangulations have d-diagonal colorings with at most 1 + 2 . colors. A similar result is proven for plane triangulations. Each of these results extends to the projective plane. Also, a lower bound for the d-diagonal chromatic number is given.

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