Vertex-disjoint cycles in bipartite tournaments (original) (raw)
2016, Electronic Notes in Discrete Mathematics
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 δ = min{δ + , δ − } at least 1.5k − 1 contains at least k vertex-disjoint 4-cycles.
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