초록 close

A tournament is an orientation of a complete graph, and in generala multipartite or c-partite tournament is an orientation of acomplete c-partite graph.In a recent article, the authors proved that a regular c-partitetournament with r ge 2 vertices in each partite set contains acycle with exactly r-1 vertices from each partite set, withexception of the case that c = 4 and r = 2. Here we willexamine the existence of cycles with r-2 vertices from eachpartite set in regular multipartite tournaments where the r-2vertices are chosen arbitrarily. Let D be a regular c-partitetournament and let X subseteq V(D) be an arbitrary set withexactly 2 vertices of each partite set. For all c ge 4 wewill determine the minimal value g(c) such that D-X isHamiltonian for every regular multipartite tournament with r geg(c).