Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903060 | Discrete Mathematics | 2018 | 6 Pages |
Abstract
Let kâ¥2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2kâ1 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 2kâ2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever kâ¥3. Finally, we show that every bipartite tournament with minimum degree δ=min{δ+,δâ} at least 1.5kâ1 contains at least k vertex-disjoint 4-cycles.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
C. Balbuena, D. González-Moreno, M. Olsen,