CYCLES THROUGH A GIVEN SET OF VERTICES IN REGULAR MULTIPARTITE TOURNAMENTS

Title & Authors
CYCLES THROUGH A GIVEN SET OF VERTICES IN REGULAR MULTIPARTITE TOURNAMENTS
Volkmann, Lutz; Winzen, Stefan;

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 $\small{r{\geq}2}$ vertices in each partite set contains a cycle with exactly r-1 vertices from each partite set, with exception of the case that c
Keywords
multipartite tournaments;regular multipartite tournaments;cycles through given set of vertices;
Language
English
Cited by
1.
Multipartite tournaments: A survey, Discrete Mathematics, 2007, 307, 24, 3097
References
1.
J. Bang-Jensen and G. Gutin, Digraphs, Theory, algorithms and applications. Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 2001

2.
Y. Guo, Semi complete Multipartite Digraphs: A Generalization of Tournaments, Habilitation thesis, RWTH Aachen (1998), 102 pp

3.
G. Gutin, Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey, J. Graph Theory 19 (1995), no. 4, 481-505

4.
G. Gutin, Note on the path covering number of a semicomplete multipartite digraph, J. Combin. Math. Combin. Comput. 32 (2000), 231-237

5.
J. W. Moon, On subtournaments of a tournament, Canad. Math. Bull. 9 (1966), 297-301

6.
O. Ore, Theory of gmphs, American Mathematical Society Colloquium Publications, Vol. 38, American Mathematical Society, 1962

7.
J. Stella, L. Volkmann, and S. Winzen, How close to regular must a multipartite tournament be to secure a given path covering number?, Ars Combinatoria, to appea

8.
P. Turan, Eine Extremalaufgabe aus der Gmphentheorie, Mat. Fiz. Lapok 48 (1941), 436-452

9.
L. Volkmann, F'undamente der Gmphentheorie, Springer Lehrbuch Mathematik, Springer-Verlag, Vienna, 1996

10.
L. Volkmann, Strong subtournaments of multipartite tournaments, Australas. J. Combin. 20 (1999), 189-196

11.
L. Volkmann, Cycles in multipartite tournaments: results and problems, Discrete Math. 245 (2002), no. 1-3, 19-53

12.
L. Volkmann and S. Winzen, Cycles with a given number of vertices from each partite set in regular multipartite tournaments, Czechoslovak Math. J. 56 (131) (2006), no. 3, 827-843

13.
L. Volkmann and S. Winzen, On the connectivity of close to regular multipartite tournaments, Discrete Appl. Math. 154 (2006), no. 9, 1437-1452

14.
L. Volkmann and S. Winzen, Almost regular c-partite tournaments contain a strong subtournaments of order c when c\${ge}\$ 5, Discrete Math., to appear

15.
S. Winzen, Close to Regular Multipartite Tournaments, Ph. D. thesis, RWTH Aachen, 2004

16.
A. Yeo, One-diregular subgmphs in semicomplete multipartite digmphs, J. Graph Theory 24 (1997), no. 2, 175-185

17.
A. Yeo, Semicomplete Multipartite Digmphs, Ph. D. thesis, Odense University, 1998

18.
A. Yeo, How close to regular must a semicomplete multipartite digmph be to secure Hamiltonicity?, Graphs Combin. 15 (1999), no. 4, 481-493