Improved bound on facial parity edge coloring

TL;DR

This paper improves the upper bound on the number of colors needed for facial parity edge coloring in 2-edge connected plane graphs from 20 to 16, advancing understanding of graph coloring constraints.

Contribution

The paper presents a tighter upper bound of 16 colors for facial parity edge coloring, improving upon the previous bound of 20.

Findings

Facial parity edge coloring can be achieved with at most 16 colors.

The new bound improves previous results by reducing the number of colors.

The method may influence future research in graph coloring and related algorithms.

Abstract

A facial parity edge coloring of a 2-edge connected plane graph is an edge coloring where no two consecutive edges of a facial walk of any face receive the same color. Additionally, for every face f and every color c either no edge or an odd number of edges incident to f are colored by c. Czap, Jendrol', Kardo\v{s} and Sotak showed that every 2-edge connected plane graph admits a facial parity edge coloring with at most 20 colors. We improve this bound to 16 colors.