List Vertex-arboricity of Planar Graphs without Intersecting 5-cycles

The vertex-arboricity a(G)of a graph G is the minimum number of colors required for a vertex coloring of G such that no cycle is monochromatic.The list vertex-arboricity al(G)is the list-coloring version of this concept.In this paper,we prove that every planar graph G without intersecting 5-cycles has al(G)≤2.This extends a result by Raspaud and Wang[On the vertex-arboricity of planar graphs,European J.Combin.29(2008),1064-1075]that every planar graph G without 5-cycles has a(G)≤2.