Vertex-dominating cycles in 2-connected bipartite graphs

A cycle C is a vertex-dominating cycle if every vertex is adjacent to some vertex of C. Bondy and Fan [4] showed that if G is a 2-connected graph with δ(G) ≥ 13 (|V (G)| − 4), then G has a vertex-dominating cycle. In this paper, we prove that if G is a 2-connected bipartite graph with partite sets V1 and V2 such that δ(G) ≥ 1 3 (max{|V1|, |V2|}+ 1), then G has a vertex-dominating cycle.