Paths with a given number of vertices from each partite set in regular multipartite tournaments |
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Authors: | Lutz Volkmann |
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Institution: | Lehrstuhl II für Mathematik, RWTH Aachen, 52056 Aachen, Germany |
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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.For c?2 we prove that a regular c-partite tournament with r?2 vertices in each partite set contains a directed path with exactly two vertices from each partite set. Furthermore, if c?4, then we will show that almost all regular c-partite tournaments D contain a directed path with exactly r-s vertices from each partite set for each given integer s∈N, if r is the cardinality of each partite set of D. Some related results are also presented. |
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Keywords: | Multipartite tournaments Regular multipartite tournaments Paths through given number of vertices |
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