A Sufficient Condition for Planar Graphs
Journal of Graph Theory
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 acyclically L-list colorable if for a given listassignment L = {L(v): v: εV}, there exists a proper acyclic coloring φ of Gsuch that φ(v) ε L(v) for allv ε V. If G is acyclicallyL-list colorable for any list assignment with |L(v)|≥ k for all v ε V, thenG is acyclically k-choosable. In this article, weprove that every planar graph G without 4- and 5-cycles, orwithout 4- and 6-cycles is acyclically 5-choosable. © 2006Wiley Periodicals, Inc. J Graph Theory 54: 245260, 2007