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Abstract: A multipartite tournament is an orientation of a complete $c$-partite graph.In L. Volkmann, A remark on cycles through an arc in strongly connectedmultipartite tournaments, Appl. Math. Lett. 20 2007 1148-1150, Volkmannproved that a strongly connected $c$-partite tournament with $c \ge 3$ containsan arc that belongs to a directed cycle of length $m$ for every $m \in \{3, 4,\ldots, c\}$. He also conjectured the existence of three arcs with thisproperty. In this note, we prove the existence of two such arcs.



Author: Alexandru I. Tomescu

Source: https://arxiv.org/







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