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Keywords:

  • acyclic edge coloring;
  • planar graph;
  • girth;
  • maximum degree

Abstract

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index inline image of G is the smallest integer k such that G has an acyclic edge coloring using k colors. Fiaminline imageik (Math. Slovaca 28 (1978), 139–145) and later Alon et al. (J Graph Theory 37 (2001), 157–167) conjectured that inline image for any simple graph G with maximum degree Δ. In this article, we confirm this conjecture for planar graphs of girth at least 4.