Weakly Complementary Cycles in 3-Connected Multipartite Tournaments

- Journal title : Kyungpook mathematical journal
- Volume 48, Issue 2, 2008, pp.287-302
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2008.48.2.287

Title & Authors

Weakly Complementary Cycles in 3-Connected Multipartite Tournaments

Volkmann, Lutz; Winzen, Stefan;

Volkmann, Lutz; Winzen, Stefan;

Abstract

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles and such that V(D) = , and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles and such that contains vertices of all partite sets of D. The problem of complementary cycles in 2-connected tournaments was completely solved by Reid [4] in 1985 and Z. Song [5] in 1993. They proved that every 2-connected tournament T on at least 8 vertices has complementary cycles of length t and - t for all . Recently, Volkmann [8] proved that each regular multipartite tournament D of order is cycle complementary. In this article, we analyze multipartite tournaments that are weakly cycle complementary. Especially, we will characterize all 3-connected c-partite tournaments with that are weakly cycle complementary.

Keywords

Multipartite tournaments;weakly cycle complementarity;

Language

English

Cited by

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