ArticleOriginal scientific text
Title
Vertex-dominating cycles in 2-connected bipartite graphs
Authors 1
Affiliations
- Department of Mathematics, School of Dentistry, Asahi University, 1851 Hozumi, Gifu 501-0296, Japan
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.
Keywords
vertex-dominating cycle, dominating cycle, bipartite graph
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Pages:
323-332
Main language of publication
English
Received
2006-04-28
Accepted
2007-02-23
Published
2007
DOI: 10.7151/dmgt.1364
Exact and natural sciences