http://dx.doi.org/10.1006/jctb.2001.2038">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On structure of some plane graphs with application to choosability

Language

English

Abstract

A graph G=(V, E) is (x, y)-choosable for integers x>y≥1 if for any given family {A(v)|v∈V} of sets A(v) of cardinality x, there exists a collection {B(v)|v∈V} of subsets B(v)⊂A(v) of cardinality y such that B(u)∩B(v)=Ø whenever uv∈E(G). 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. © 2001 Academic Press.

Keywords

Choosable; plane graph; cycle; triangle

Publication Date

2001

Source Publication Title

Journal of Combinatorial Theory, Series B

Volume

82

Issue

2

Start Page

285

End Page

296

Publisher

Elsevier

ISSN (print)

00958956

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