An extension of Thomassen's result on choosability

Abstract

Thomassen proved that all planar graphs are $5$-choosable. Škrekovski strengthened the result by showing that all $K_5$-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 $K_5$-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.

7 pages; 1 figure

References in corpus (2)

• Thomassen's Choosability Argument Revisited
• Cover and variable degeneracy

Cited by in corpus (2)

• Planar graphs without normally adjacent short cycles
• Variable degeneracy on toroidal graphs