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Vertex-disjoint cycles in bipartite tournaments

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Vertex_disjoint_4-cycles_in_bipartite_tournaments.pdf (297,2Kb)
 
10.1016/j.disc.2017.10.023
 
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hdl:2117/111583

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González Moreno, Diego
Balbuena Martínez, Maria Camino TeófilaMés informacióMés informacióMés informació
Olsen, Mika
Document typeArticle
Defense date2016-10
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
Let k=2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k-1 contains k vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least 2k-2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever k=3. Finally, we show that every bipartite tournament with minimum degree d=min(d+,d-) at least 1.5k-1 contains at least k vertex-disjoint 4-cycles.
CitationGonzález-Moreno, D., Balbuena, C., Olsen, M. Vertex-disjoint cycles in bipartite tournaments. "Discrete mathematics", Octubre 2016, vol. 54, p. 69-72. 
URIhttp://hdl.handle.net/2117/111583
DOI10.1016/j.disc.2017.10.023
ISSN0012-365X
Publisher versionhttp://www.sciencedirect.com/science/article/pii/S157106531630107X
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