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.