List edge coloring of outer-1-planar graphs

TL;DR

This paper proves that outer-1-planar graphs with maximum degree 4 and crossing distance at least 3 have their list edge chromatic number equal to their maximum degree, extending known results for higher degrees.

Contribution

It establishes the equality of list edge chromatic number and maximum degree for a new class of outer-1-planar graphs with degree 4 and crossing distance at least 3.

Findings

List edge chromatic number equals maximum degree for these graphs.

Extends known results from degree ≥ 5 to degree 4 under certain conditions.

Provides new insights into edge coloring of outer-1-planar graphs.

Abstract

A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number $\chi'_l(G)$ of any outer-1-planar graph $G$ with maximum degree $\Delta(G)\geq 5$ is exactly its maximum degree. In this paper, we prove $\chi'_l(G)=\Delta(G)$ for outer-1-planar graphs $G$ with $\Delta(G)=4$ and with the crossing distance being at least 3.