Vertex-dominating cycles in 2-connected bipartite graphs

• Autorzy: Tomoki Yamashita
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

vertex-dominating cycle; dominating cycle; bipartite graph

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 2
• Strony: 323-332

Daty

wydano

2007

otrzymano

2006-04-28

poprawiono

2007-02-23

zaakceptowano

2007-02-23

Twórcy

autor

Tomoki Yamashita

• Department of Mathematics, School of Dentistry, Asahi University, 1851 Hozumi, Gifu 501-0296, Japan

Bibliografia

• [1] P. Ash and B. Jackson, Dominating cycles in bipartite graphs, in: Progress in Graph Theory, 1984, 81-87.
• [2] D. Bauer, H.J. Veldman, A. Morgana and E.F. Schmeichel, Long cycles in graphs with large degree sum, Discrete Math. 79 (1989/90) 59-70, doi: 10.1016/0012-365X(90)90055-M.
• [3] J.A. Bondy, Longest paths and cycles in graphs with high degree, Research Report CORR 80-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada (1980).
• [4] J.A. Bondy and G. Fan, A sufficient condition for dominating cycles, Discrete Math. 67 (1987) 205-208, doi: 10.1016/0012-365X(87)90029-X.
• [5] R. Diestel, Graph Theory, (2nd ed.) (Springer-Verlag, 2000).
• [6] H.A. Jung, On maximal circuits in finite graphs, Ann. Discrete Math. 3 (1978) 129-144, doi: 10.1016/S0167-5060(08)70503-X.
• [7] J. Moon and L. Moser, On hamiltonian bipartite graphs, Israel J. Math. 1 (1963) 163-165, doi: 10.1007/BF02759704.
• [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.
• [10] H. Wang, On Long Cycles in a 2-connected Bipartite Graph, Graphs and Combin. 12 (1996) 373-384, doi: 10.1007/BF01858470.

Identyfikatory

DOI

10.7151/dmgt.1364