Acyclic edge coloring of planar graphs

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index of G, denoted by chi(a)' (G), is the smallest integer k such that G is acyclically edge k-colorable. In this paper, we consider the planar graphs without 3-cycles and intersecting 4-cycles, and prove that chi(a)' (G) <= Delta(G) + 1 if Delta(G) >= 8.

Automated summary

In this paper, we investigate the acyclic chromatic index of planar graphs without 3-cycles and intersecting 4-cycles. We prove that the acyclic chromatic index is less than or equal to the maximum degree plus 1 when the maximum degree is greater than or equal to 8.