Cycles Containing a Given Arc in Regular Multipartite Tournaments
โ Scribed by Guo-fei Zhou; Ke-min Zhang
- Publisher
- Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2002
- Tongue
- English
- Weight
- 104 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0168-9673
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A multipartite or c-partite tournament is an orientation of a complete c-partite graph. In this note we prove that a strongly connected c-partite tournament with c โฅ 3 contains an arc that belongs to a directed cycle of length m for every m โ {3, 4, . . . , c}.
Volkmann [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007Lett. 20 ( ) 1148Lett. 20 ( -1150] ] conjectured that a strong c-partite tournament with c โฅ 3 contains three arcs that belong to a cycle of length m for each m โ {3, 4,
Let (x, y) be a specified arc in a k-regular bipartite tournament B. We prove that there exists a cycle C of length four through (x, y) in B such that B-C is hamiltonian.