Vertex-arboricity of planar graphs without intersecting triangles

The vertex-arboricity a(G) of a graph G is the minimum number of subsets into which vertex set V(G) can be partitioned so that each subset induces an acyclic graph. In this paper, we prove one of the conjectures proposed by Raspaud and Wang (2008) [15] which says that a(G)=2 for any planar graph without intersecting triangles.