An improved bound on acyclic chromatic index of planar graphs

作者:Guan, Yue; Hou, Jianfeng*; Yang, Yingyuan
来源:Discrete Mathematics, 2013, 313(10): 1098-1103.
DOI:10.1016/j.disc.2013.02.002

摘要

A proper edge coloring of a graph G is called acyclic if there is no bichromatic cycle in G. The acyclic chromatic index of G, denoted by chi'(a)(G), is the least number of colors k such that G has an acyclic k-edge-coloring. Basavaraju et al. [M. Basavaraju, L.S. Chandran, N. Cohen, F. Havet and T. Muller, Acyclic edge-coloring of planar graphs, SIAM journal of Discrete Mathematics 25 (2) (2011)463-478] showed that chi'(a)(G) <= Delta(G) + 12 for any planar graph G with maximum degree Delta(G). In this paper, the bound is improved to Delta(G) + 10.

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