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. Fiam?ik (Math. Slovaca 28 (1978), 139-145) and later Alon et al. (J Graph Theory 37 (2001), 157-167) conjectured that a′(G)≤Δ+2 for any simple graph G with maximum degree Δ. In this article, we confirm this conjecture for planar graphs of girth at least 4.
展开▼
机译：图G的无环边缘着色是适当的边缘着色，使得不产生双色循环。 G的非循环色标a'（G）是最小的整数k，使得G具有使用k种颜色的非循环边缘着色。 Fiam？ik（Math。Slovaca 28（1978），139-145）和后来的Alon等。 J Graph Theory 37（2001），157-167）推测，对于任何具有最大程度Δ的简单图形G，a'（G）≤Δ+ 2。在本文中，我们至少对周长的平面图确认了这个猜想。
展开▼
