List vertex arboricity of planar graphs without 5-cycles intersecting with 6-cycles

The vertex arboricity a(G) of a graph G is the minimum number of colors required to color the vertices of G such that no cycle is monochromatic. The list vertex arboricity al(G) is the list version of this concept. In this paper, we prove that if G is a planar graph without 5-cycles intersecting with 6-cycles, then al(G)≤2.