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Cycles with a given number of vertices from each partite set in regular multipartite tournaments

Lutz Volkmann; Stefan Winzen — 2006

Czechoslovak Mathematical Journal

If $x$ is a vertex of a digraph $D$ , then we denote by $d^{+} (x)$ and $d^{-} (x)$ the outdegree and the indegree of $x$ , respectively. A digraph $D$ is called regular, if there is a number $p \in ℕ$ such that $d^{+} (x) = d^{-} (x) = p$ for all vertices $x$ of $D$ . A $c$ -partite tournament is an orientation of a complete $c$ -partite graph. There are many results about directed cycles of a given length or of directed cycles with vertices from a given number of partite sets. The idea is now to combine the two properties. In this article, we examine in particular, whether...

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