An extension of Thomassen’s result on choosability

摘要

Thomassen proved that all planar graphs are 5-choosable. Škrekovski strengthened the result by showing that all K5-minor-free graphs are 5-choosable. Dvořák and Postle pointed out that all planar graphs are DP-5-colorable. In this note, we first improve these results by showing that every K5-minor-free or K3,3-minor-free graph is DP-5-colorable. In the final section, we further improve these results under the term strictly f-degenerate transversal.