Acyclic edge coloring of planar graphs without 5-cycles

Authors:
Qiaojun Shu;Weifan Wang;Yiqiao Wang
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Academy of Mathematics and Systems Science, Beijing 100080, China
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index a^'(G) of G is the smallest integer k such that G has an acyclic edge coloring using k colors. Fiamcik (1978) [9] and later Alon et al. (2001) [2] conjectured that a^'(G)@?@D+2 for any simple graph G with maximum degree @D. In this paper, we confirm this conjecture for planar graphs without 5-cycles.