Vertex-disjoint cycles in bipartite tournaments
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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.