An improved bound on acyclic chromatic index of planar graphs

TL;DR

This paper improves the upper bound on the acyclic chromatic index of planar graphs from (G)+12 to (G)+10, advancing understanding of edge colorings in planar graph theory.

Contribution

The paper presents a tighter bound on the acyclic chromatic index of planar graphs, reducing the previous bound by two.

Findings

Bound on (G)+10 established for planar graphs

Improves previous bound of (G)+12

Advances theoretical understanding of acyclic edge coloring

Abstract

Proper edge coloring of a graph $G$ is called acyclic if there is no bichromatic cycle in $G$. The acyclic chromatic index of $G$, denoted by $\chi'_a(G)$, is the least number of colors $k$ such that $G$ has an acyclic edge $k$-coloring. Basavaraju et al. [Acyclic edge-coloring of planar graphs, SIAM J. Discrete Math. 25 (2) (2011), 463--478] showed that $\chi'_a(G)\le \Delta(G)+12$ for planar graphs $G$ with maximum degree $\Delta(G)$. In this paper, the bound is improved to $\Delta(G)+10$.