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 ${\chi }_a^{{}^{\prime }}(G)$, 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 ${\chi }_a^{{}^{\prime }}(G)\le \mathrm{\Delta }(G)+1$ if $\mathrm{\Delta }(G)\ge 8$.