English

On cycles through two arcs in strong multipartite tournaments

Discrete Mathematics 2010-06-07 v1

Abstract

A multipartite tournament is an orientation of a complete cc-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148--1150], Volkmann proved that a strongly connected cc-partite tournament with c3c \ge 3 contains an arc that belongs to a directed cycle of length mm for every m{3,4,,c}m \in \{3, 4, \ldots, c\}. He also conjectured the existence of three arcs with this property. In this note, we prove the existence of two such arcs.

Cite

@article{arxiv.1006.0902,
  title  = {On cycles through two arcs in strong multipartite tournaments},
  author = {Alexandru I. Tomescu},
  journal= {arXiv preprint arXiv:1006.0902},
  year   = {2010}
}
R2 v1 2026-06-21T15:32:06.249Z