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A sufficient condition for planar graphs to be acyclically 5‐choosable
Author(s) -
Chen Min,
Raspaud André
Publication year - 2012
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20604
Subject(s) - combinatorics , planar graph , mathematics , vertex (graph theory) , graph , list coloring , discrete mathematics , graph power , line graph
A proper vertex coloring of a graph G = ( V, E ) is acyclic if G contains no bicolored cycle. Given a list assignment L = { L ( v )| v ∈ V } of G , we say G is acyclically L ‐list colorable if there exists a proper acyclic coloring π of G such that π( v )∈ L ( v ) for all v ∈ V . If G is acyclically L ‐list colorable for any list assignment with | L ( v )|≥ k for all v ∈ V , then G is acyclically k ‐choosable. In this article we prove that every planar graph without 4‐cycles and without intersecting triangles is acyclically 5‐choosable. This improves the result in [M. Chen and W. Wang, Discrete Math 308 (2008), 6216–6225], which says that every planar graph without 4‐cycles and without two triangles at distance less than 3 is acyclically 5‐choosable. © 2011 Wiley Periodicals, Inc. J Graph Theory