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On the acyclic choosability of graphs

✍ Scribed by Mickaël Montassier; Pascal Ochem; André Raspaud

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 348 KB
Volume: 51
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20134

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✦ Synopsis

Abstract

A proper vertex coloring of a graph G = (V,E) is acyclic if G contains no bicolored cycle. A graph G is L‐list colorable if for a given list assignment L = {L(v): v ∈ V}, there exists a proper coloring c of G such that c (v) ∈ L(v) for all v ∈ V. If G is L‐list colorable for every list assignment with |L (v)| ≥ k for all v ∈ V, then G is said k‐choosable. A graph is said to be acyclically k‐choosable if the obtained coloring is acyclic. In this paper, we study the links between acyclic k‐choosability of G and Mad(G) defined as the maximum average degree of the subgraphs of G and give some observations about the relationship between acyclic coloring, choosability, and acyclic choosability. © 2005 Wiley Periodicals, Inc. J Graph Theory 51: 281–300, 2006

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