Geodesic
Vertex-dominating cycles in 2-connected bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 323-332

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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) ≥ 1/3(|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.
Keywords: vertex-dominating cycle, dominating cycle, bipartite graph 
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Yamashita, Tomoki. Vertex-dominating cycles in 2-connected bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 323-332. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a8/