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Vertex-dominating cycles in 2-connected bipartite graphs. (English) Zbl 1133.05051

Summary: A cycle \(C\) is a vertex-dominating cycle if every vertex is adjacent to some vertex of J. A. Bondy and G. Fan [Discrete Math. 67, 205–208 (1987; Zbl 0634.05045)] showed that if \(G\) is a 2-connected graph with \(\delta (G)\geq \frac13(|V(G)|-4)\), then \(G\) has a vertex-dominating cycle. In this paper, we prove that if \(G\) is a 2-connected bipartite graph with partite sets \(V_1\) and \(V_2\) such that \(\delta(G)\geq \frac13 (\max\{|V_1|,|V_2|\}+1)\), then \(G\) has a vertex-dominating cycle.

MSC:

05C38 Paths and cycles
05C45 Eulerian and Hamiltonian graphs

Citations:

Zbl 0634.05045
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