List Vertex Arboricity of Graphs Without Forbidden Minors

Abstract

The notions of $L$-tree-coloring and list vertex arboricity of graphs are introduced in the paper, while a sufficient condition for a plane graph admitting an $L$-tree-coloring is given. Further, it is proved that every graph without $K_5$-minors or $K_{3,3}$-minors has list vertex arboricity at most $3$, and this upper bound is sharp.