# Vertex-dominating cycles in 2-connected bipartite graphs

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 2, page 323-332
- ISSN: 2083-5892

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topTomoki Yamashita. "Vertex-dominating cycles in 2-connected bipartite graphs." Discussiones Mathematicae Graph Theory 27.2 (2007): 323-332. <http://eudml.org/doc/270355>.

@article{TomokiYamashita2007,

abstract = {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.},

author = {Tomoki Yamashita},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {vertex-dominating cycle; dominating cycle; bipartite graph},

language = {eng},

number = {2},

pages = {323-332},

title = {Vertex-dominating cycles in 2-connected bipartite graphs},

url = {http://eudml.org/doc/270355},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Tomoki Yamashita

TI - Vertex-dominating cycles in 2-connected bipartite graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 2

SP - 323

EP - 332

AB - 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.

LA - eng

KW - vertex-dominating cycle; dominating cycle; bipartite graph

UR - http://eudml.org/doc/270355

ER -

## References

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- [8] O. Ore, Note on Hamilton circuits, Amer. Math. Monthly 67 (1960) 55, doi: 10.2307/2308928.
- [9] A. Saito and T. Yamashita, A Note on Dominating Cycles in Tough Graphs, Ars Combinatoria 69 (2003) 3-8. Zbl1073.05558
- [10] H. Wang, On Long Cycles in a 2-connected Bipartite Graph, Graphs and Combin. 12 (1996) 373-384, doi: 10.1007/BF01858470. Zbl0864.05051

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