On Cycles in Multipartite Tournaments

An n-partite tournament is an orientation of a complete n-partite graph. We show that if D is a strongly connected n-partite tournament, and if v is the only vertex in one of the partite sets of D, then for any m, 3 ≤ m ≤ n, there is an m-cycle of D containing v. This generalizes a theorem of Moon....

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Bibliographic Details
Published inJournal of combinatorial theory. Series B Vol. 58; no. 2; pp. 319 - 321
Main Author Gutin, G.
Format Journal Article
LanguageEnglish
Published Duluth, MN Elsevier Inc 01.07.1993
Academic Press
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Multipartite graph
Complete graph
Tournament
Cycle(graph)
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Summary:An n-partite tournament is an orientation of a complete n-partite graph. We show that if D is a strongly connected n-partite tournament, and if v is the only vertex in one of the partite sets of D, then for any m, 3 ≤ m ≤ n, there is an m-cycle of D containing v. This generalizes a theorem of Moon.
ISSN:0095-8956
1096-0902
DOI:10.1006/jctb.1993.1047