M ar 2 00 8 Acyclic Edge Coloring with ∆ + o ( ∆ ) Colors
نویسنده
چکیده
A proper edge coloring of a graph G is said to be acyclic if every cycle of G receives at least three colors. The acyclic edge chromatic number of G, denoted a(G), is the least number of colors in an acyclic edge coloring of G. Alon, Sudakov and Zaks [Acyclic edge coloring of graphs, J. Graph Theory 37 (2001), 157-167] conjectured that a(G) ≤ ∆(G) + 2 holds for any graph G. In present paper, we prove that a(G) is bounded by ∆ + o(∆) for any graph G. Our argument is probabilistic.
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