科研之友
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摘要
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 (Math. Slovaca 28 (1978), 139-145) and later Alon et al. (J Graph Theory 37 (2001), 157-167) conjectured that a(G)+2 for any simple graph G with maximum degree . In this article, we confirm this conjecture for planar graphs of girth at least 4.
