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

Lutz VolkmannStefan 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 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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