An extension of Thomassen's result on choosability

Abstract

Thomassen proved that every planar graph is 5-choosable. Škrekovski [8] strengthened it by showing that every K5-minor-free graph is 5-choosable. Dvořák and Postle observed that every planar graph is DP-5-colorable. In this note, we first improve these results by showing that every K5-minor-free graph is DP-5-colorable, and every 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.