# CYCLES THROUGH A GIVEN SET OF VERTICES IN REGULAR MULTIPARTITE TOURNAMENTS

• Volkmann, Lutz ;
• Winzen, Stefan
• Published : 2007.05.31
• 76 2

#### Abstract

A tournament is an orientation of a complete graph, and in general a multipartite or c-partite tournament is an orientation of a complete c-partite graph. In a recent article, the authors proved that a regular c-partite tournament with $r{\geq}2$ vertices in each partite set contains a cycle with exactly r-1 vertices from each partite set, with exception of the case that c=4 and r=2. Here we will examine the existence of cycles with r-2 vertices from each partite set in regular multipartite tournaments where the r-2 vertices are chosen arbitrarily. Let D be a regular c-partite tournament and let $X{\subseteq}V(D)$ be an arbitrary set with exactly 2 vertices of each partite set. For all $c{\geq}4$ we will determine the minimal value g(c) such that D-X is Hamiltonian for every regular multipartite tournament with $r{\geq}g(c)$.

#### Keywords

multipartite tournaments;regular multipartite tournaments;cycles through given set of vertices

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#### Cited by

1. Multipartite tournaments: A survey vol.307, pp.24, 2007, https://doi.org/10.1016/j.disc.2007.03.053