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 -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 -partite tournament with contains an arc that belongs to a directed cycle of length for every . 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}
}