Every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable
Information Processing Letters
Note: A note on the acyclic 3-choosability of some planar graphs
Discrete Applied Mathematics
Acyclic choosability of graphs with small maximum degree
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
A polyhedral study of the acyclic coloring problem
Discrete Applied Mathematics
Planar graphs without 4- and 5-cycles are acyclically 4-choosable
Discrete Applied Mathematics
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A proper vertex coloring of a graph G = (V,E) isacyclic if G contains no bicolored cycle. A graph Gis L-list colorable if for a given list assignment L= {L(v): v ε V}, there exists a propercoloring c of G such that c (v)ε L(v) for all v ε V.If G is L-list colorable for every list assignmentwith |L (v)| ≥ k for all v εV, then G is said k-choosable. A graph is saidto be acyclically k-choosable if the obtained coloring isacyclic. In this paper, we study the links between acyclick-choosability of G and Mad(G) definedas the maximum average degree of the subgraphs of G and givesome observations about the relationship between acyclic coloring,choosability, and acyclic choosability. © 2005 WileyPeriodicals, Inc. J Graph Theory 51: 281300, 2006