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On Structure of Some Plane Graphs with Application to Choosability

✍ Scribed by Peter Che Bor Lam; Wai Chee Shiu; Baogang Xu

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 180 KB
Volume: 82
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2038

No coin nor oath required. For personal study only.

✦ Synopsis

A graph G=(V, E) is (x, y)-choosable for integers x> y 1 if for any given family

In this paper, structures of some plane graphs, including plane graphs with minimum degree 4, are studied. Using these results, we may show that if G is free of k-cycles for some k # [3,4,5,6], or if any two triangles in G have distance at least 2, then G is (4m, m)-choosable for all nonnegative integers m. When m=1, (4m, m)-choosable is simply 4-choosable. So these conditions are also sufficient for a plane graph to be 4-choosable.

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