A note on the edge choosability of $K_{5}$-minor free graphs

TL;DR

This paper extends known results on edge-choosability from planar graphs to $K_5$-minor free graphs, establishing new bounds for their edge-choosability based on maximum degree.

Contribution

The paper generalizes edge-choosability bounds from planar graphs to $K_5$-minor free graphs, providing new theoretical insights.

Findings

Extended edge-choosability bounds to $K_5$-minor free graphs.

Established that $K_5$-minor free graphs are $( ext{max degree}+1)$-edge-choosable under certain conditions.

Connected results to previous planar graph bounds.

Abstract

For a planar graph $G$, Borodin stated that $G$ is $(\Delta+1)$-edge-choosable if $\Delta \geq9$ and later Bonamy showed that $G$ is $9$-edge-choosable if $\Delta=8$. At the same time, Borodin et al. proved that $G$ is $\Delta$-edge-choosable if $\Delta\geq12$. In the paper, we extend these results to $K_5$-minor free graphs.