科研之友
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摘要
A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a'(G), is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that a'(G) acurrency sign Delta(G) + 2 for any graphs. In this paper, it is shown that the conjecture holds for planar graphs without 4- and 5-cycles or without 4- and 6-cycles.
