Opuscula Math. 29, no. 4 (2009), 345-364
http://dx.doi.org/10.7494/OpMath.2009.29.4.345

Opuscula Mathematica

# Cyclability in bipartite graphs

Denise Amar
Evelyne Flandrin
Grzegorz Gancarzewicz

Abstract. Let $$G=(X,Y,E)$$ be a balanced $$2$$-connected bipartite graph and $$S \subset V(G)$$. We will say that $$S$$ is cyclable in $$G$$ if all vertices of $$S$$ belong to a common cycle in $$G$$. We give sufficient degree conditions in a balanced bipartite graph $$G$$ and a subset $$S \subset V(G)$$ for the cyclability of the set $$S$$.

Keywords: graphs, cycles, bipartite graphs.

Mathematics Subject Classification: 05C20, 05C35, 05C38, 05C45.

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• Denise Amar
• LaBRI Université de Bordeaux 1, 351 Coursde la Liberation, 33405 Talence, France
• Evelyne Flandrin
• LRI, UMR8623, Bâtiment 490, Université Paris-Sud, 91405 Orsay Cedex France
• Grzegorz Gancarzewicz
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
• Revised: 2009-07-01.
• Accepted: 2009-07-23.