Geodesic
Vertex-dominating cycles in 2-connected bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 323-332.

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGT_2007_27_2_a8,
     author = {Yamashita, Tomoki},
     title = {Vertex-dominating cycles in 2-connected bipartite graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {323--332},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a8/}
}
TY  - JOUR
AU  - Yamashita, Tomoki
TI  - Vertex-dominating cycles in 2-connected bipartite graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 323
EP  - 332
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a8/
LA  - en
ID  - DMGT_2007_27_2_a8
ER  - 
%0 Journal Article
%A Yamashita, Tomoki
%T Vertex-dominating cycles in 2-connected bipartite graphs
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 323-332
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a8/
%G en
%F DMGT_2007_27_2_a8
Yamashita, Tomoki. Vertex-dominating cycles in 2-connected bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 323-332. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a8/

[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.