Defective choosability of graphs in surfaces

Douglas Woodall

ArticleOriginal scientific text

Title

Defective choosability of graphs in surfaces

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Affiliations

School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK

Abstract

It is known that if G is a graph that can be drawn without edges crossing in a surface with Euler characteristic ε, and k and d are positive integers such that k ≥ 3 and d is sufficiently large in terms of k and ε, then G is (k,d)*-colorable; that is, the vertices of G can be colored with k colors so that each vertex has at most d neighbors with the same color as itself. In this paper, the known lower bound on d that suffices for this is reduced, and an analogous result is proved for list colorings (choosability). Also, the recent result of Cushing and Kierstead, that every planar graph is (4,1)*-choosable, is extended to

K_{3, 3}

-minor-free and K₅-minor-free graphs.

Keywords

ENG

list coloring, defective coloring, minor-free graph

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Title

Defective choosability of graphs in surfaces

Affiliations

Abstract

Keywords

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