A note on the edge choosability of $K_5$-minor free graphs

Abstract

For a planar graph $G$, Borodin stated that $G$ is $(\hat{I}”+1)$-edge-choosable if $\hat{I}”\ge 9$ and later Bonamy showed that $G$ is $9$-edge-choosable if $\hat{I}”=8$. At the same time, Borodin et al. proved that $G$ is $\hat{I}”$-edge-choosable if $\hat{I}”\ge 12$. In the paper, we extend these results to $K_5$-minor free graphs.