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.
1970-2025 CP (Manitoba, Canada) unless otherwise stated.