Acyclic Edge Coloring of Planar Graphs without Adjacent Triangles

Abstract:

      An acyclic edge coloring of a graph $G$ is a proper edge coloring such that there are no bichromatic cycles. The \emph{acyclic edge chromatic number} of a graph $G$ is the minimum number $k$ such that there exists an acyclic edge coloring using $k$ colors and is denoted by $\chi'_{a}(G)$. In this paper we prove that $\chi'_{a}(G)\leq \Delta(G)+5$ for planar graphs $G$ without adjacent triangles.