Further result on acyclic chromatic index of planar graphs

TL;DR

This paper proves that every planar graph can be acyclically edge colored using at most six more colors than its maximum degree, advancing understanding of acyclic chromatic indices.

Contribution

The paper establishes an upper bound of (G)+6 colors for acyclic edge coloring of all planar graphs, improving previous bounds.

Findings

Every planar graph admits an acyclic edge coloring with (G)+6 colors.

The result narrows the gap towards the conjectured (G)+2 bound.

Provides new techniques for acyclic edge coloring of planar graphs.

Abstract

An acyclic edge coloring of a graph $G$ is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index $\chiup_{a}'(G)$ of a graph $G$ is the least number of colors in an acyclic edge coloring of $G$. It was conjectured that $\chiup'_{a}(G)\leq \Delta(G) + 2$ for any simple graph $G$ with maximum degree $\Delta(G)$. In this paper, we prove that every planar graph $G$ admits an acyclic edge coloring with $\Delta(G) + 6$ colors.