Displaying similar documents to “On the identification of vertices using cycles.”

Vertex-dominating cycles in 2-connected bipartite graphs

Tomoki Yamashita (2007)

Discussiones Mathematicae Graph Theory

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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.

Large Degree Vertices in Longest Cycles of Graphs, I

Binlong Li, Liming Xiong, Jun Yin (2016)

Discussiones Mathematicae Graph Theory

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In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.