| An induced forest κ-partition of a graph G is a κ-partition (Vi,V2,…,Vκ) of the vertex set V(G) such that, for each i with1≤i<κ, the induced subgraph G[Vi]is a forest. The vertex arboricity of a graph G is the minimum positive integer k such that G has an induced forest κ-partition.The vertex arboricity is an important graph parameter in the research of graph theory. In the literature, it has been shown that every planar graph of diameter2has a vertex arboricity of at most2. The κ5-minor-free graph studied in this paper is a generalization of the planar graph.We show in this paper that every κ5-minor-free graph of diameter2has a vertex arboricity of at most2. |
