An extension of Thomassen's result on choosability

TL;DR

This paper extends known results on the choosability of minor-free graphs by proving they are DP-5-colorable and introduces improvements under the concept of strictly f-degenerate transversals.

Contribution

It proves that K5-minor-free and K3,3-minor-free graphs are DP-5-colorable, extending Thomassen's and Skrekovski's results, and further refines these results using strictly f-degenerate transversals.

Findings

K5-minor-free graphs are DP-5-colorable

K3,3-minor-free graphs are DP-5-colorable

Enhanced results via strictly f-degenerate transversal

Abstract

Thomassen proved that all planar graphs are $5$-choosable. \v{S}krekovski strengthened the result by showing that all $K_{5}$-minor-free graphs are $5$-choosable. Dvo\v{r}\'{a}k and Postle pointed out that all planar graphs are DP-$5$-colorable. In this note, we first improve these results by showing that every $K_{5}$-minor-free or $K_{3, 3}$-minor-free graph is DP-$5$-colorable. In the final section, we further improve these results under the term strictly $f$-degenerate transversal.