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Weakly Hamiltonian-connected ordinary multipartite tournaments

Jørgen Bang-Jensen, Gregory Gutin, Jing Huang
1995 Discrete Mathematics  
multipartite tournament and finds one, if it exists.  ...  We characterize weakly Hamiltonian-connected ordinary multipartite tournaments.  ...  We point out that Theorem 3.1 does not extend to general multipartite tournaments.  ... 
doi:10.1016/0012-365x(94)00188-o fatcat:ljg6heqtubc5pkwoidbozrwwra

Cycles through a given arc and certain partite sets in strong multipartite tournaments

Hongwei Li, Shengjia Li, Yubao Guo, Qiaoping Guo
2013 The Australasian Journal of Combinatorics  
In this paper, we extend the result of Moon and prove that if D is a strong c-partite tournament with c ≥ 3, then D contains a cycle C containing vertices from exactly c partite sets such that C contains  ...  System Sci. 19 (1994), 207-214] showed that every strong tournament contains a Hamiltonian cycle through at least three pancyclic arcs.  ...  It is interesting to extend the most basic and important results on tournaments to multipartite tournaments.  ... 
dblp:journals/ajc/LiLGG13 fatcat:4xmo7qv5ezakjddeavmvbxl75a

Problems and conjectures concerning connectivity, paths, trees and cycles in tournament-like digraphs

Jørgen Bang-Jensen
2009 Discrete Mathematics  
In this paper we collect a substantial number of challenging open problems and conjectures on connectivity, paths, trees and cycles in tournaments and classes of digraphs which contain tournaments as a  ...  We also mention problems for general digraphs when they are relevant in the context.  ...  The author thanks Pavol for many interesting discussions on tournament-like digraphs.  ... 
doi:10.1016/j.disc.2008.04.016 fatcat:wlyefmsjmfgo7k36elsnozmcwm

Generalizations of tournaments: A survey

J�rgen Bang-Jensen, Gregory Gutin
1998 Journal of Graph Theory  
We describe, among numerous other topics mostly related to paths and cycles, results on hamiltonian paths and cycles.  ...  We survey results concerning various generalizations of tournaments. The reader will see that tournaments are by no means the only class of directed graphs with a very rich structure.  ...  In this paper it is shown how one can obtain a highly non-trivial result on tournaments using a result on cycles in semicomplete multipartite digraphs.  ... 
doi:10.1002/(sici)1097-0118(199808)28:4<171::aid-jgt1>3.0.co;2-g fatcat:urwonpylavfwzelzhggoojzk74

Multipartite tournaments: A survey

Lutz Volkmann
2007 Discrete Mathematics  
In this survey we mainly describe results on directed cycles and paths in strongly connected c-partite tournaments for c 3. In addition, we include about 40 open problems and conjectures.  ...  A multipartite or c-partite tournament is an orientation of a complete c-partite graph.  ...  The If for each pair of partite sets in a multipartite tournament, the arcs have a common orientation from one partite set to the other, then the digraph is a uniform multipartite tournament or an extended  ... 
doi:10.1016/j.disc.2007.03.053 fatcat:25sft4ap2zat5o3iocbum4w3zy

Cycles in multipartite tournaments: results and problems

Lutz Volkmann
2002 Discrete Mathematics  
Many results about cycles in tournaments are known, but closely related problems involving cycles in multipartite tournaments have received little attention until recently.  ...  A tournament is an orientation of a complete graph, and in general a multipartite tournament is an orientation of a complete n-partite graph.  ...  Hammer for the wonderful idea and for his kind encouragement to publish this paper in the "Perspectives" section.  ... 
doi:10.1016/s0012-365x(01)00419-8 fatcat:rg3yfj4nazaj5afljiv4hbyrvq

A sufficient condition for a semicomplete multipartite digraph to be Hamiltonian

Jørgen Bang-Jensen, Gregory Gutin, Jing Huang
1996 Discrete Mathematics  
We show that this condition is general enough to provide easy proofs of many existing results on paths and cycles in multipartite tournaments.  ...  Using this condition, we obtain a best possible lower bound on the length of a longest cycle in any strongly connected multipartite tournament.  ...  Bipartite tournaments have been studied intensively in the pursuit for tournament-like properties. Many properties have been shown to extend to bipartite tournaments, see e.g. [2, 11] .  ... 
doi:10.1016/0012-365x(95)00272-x fatcat:cqhpnnleyjg7ll3w75foe4mvrm

Pushing the cycles out of multipartite tournaments

Jing Huang, Gary MacGillivray, Kathryn L.B. Wood
2001 Discrete Mathematics  
Here we characterize, in terms of forbidden subdigraphs, the multipartite tournaments which can be made acyclic (resp. ordinary, unidirectional) using the push operation.  ...  This implies that the problem of deciding if a given multipartite tournament can be made acyclic (resp. ordinary, unidirectional) using the push operation and, if so, ÿnding a suitable subset of vertices  ...  Preliminaries and the characterization of acyclically pushable bipartite tournaments are given in Section 2. Section 3 extends these results to multipartite tournaments.  ... 
doi:10.1016/s0012-365x(00)00324-1 fatcat:idyrdrd5xfb6hotdknx4qc4mui

Page 2339 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
This result extends Alspach’s theorem for regular tournaments to regular multipartite tournaments.  ...  We also examine the structure of cycles through arcs in regular multipartite tournaments.” 2003d:05099 05C20 05C35 05C38 Tewes, Meike (D-BRGF-TM; Freiberg) Pancyclic orderings of in-tournaments.  ... 

Hamiltonian paths, containing a given path or collection of arcs, in close to regular multipartite tournaments

Lutz Volkmann, Anders Yeo
2004 Discrete Mathematics  
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.  ...  As an application of this theorem, we prove that each arc of a regular multipartite tournament is contained in a Hamiltonian path. Some related results are also presented.  ...  Let D be a multipartite tournament with a cycle-factor.  ... 
doi:10.1016/j.disc.2003.07.013 fatcat:cx6uyaournawffs6s4gh6mxuum

The cycle structure of regular multipartite tournaments

Yubao Guo, Jin Ho Kwak
2002 Discrete Applied Mathematics  
This result extends Alspach's theorem for regular tournaments to regular multipartite tournaments. We also examine the structure of cycles through arcs in regular multipartite tournaments. ?  ...  In this paper, we prove that if the cardinality common to all partite sets of a regular n-partite (n ¿ 3) tournament T is odd, then every arc of T is in a cycle that contains vertices from exactly m partite  ...  The structure of cycles in multipartite tournaments has been well studied (see [3] [4] [5] [6] [7] [8] 10] ).  ... 
doi:10.1016/s0166-218x(01)00285-2 fatcat:4pajjpyih5gh5arg4ezzhjh5dm

Outpaths in semicomplete multipartite digraphs

Yubao Guo
1999 Discrete Applied Mathematics  
This result extends a theorem of Alspach (Canad. Math. Bull. 10 (1967) 283-286) for regular tournaments to regular multipartite tournaments. ? 0166-218X/99/$ -see front matter ?  ...  An outpath of a vertex x (an arc xy, respectively) in a digraph is a directed path starting at x (xy, respectively) such that x dominates the endvertex of the path only if the endvertex also dominates  ...  The structure of cycles in semicomplete multipartite digraphs (in particular, in multipartite tournaments) has been well studied (see [6] ).  ... 
doi:10.1016/s0166-218x(99)00080-3 fatcat:apzve4koz5d6pmdzyajidrxkj4

Componentwise Complementary Cycles in Almost Regular 3-Partite Tournaments [chapter]

Zhihong He, Guojun Li, Dawei Ding, Quanhui Liu
2007 Lecture Notes in Computer Science  
In this paper, we consider a special kind of multipartite tournaments which are almost regular 3-partite tournaments, and we show that each almost regular 3partite tournament D is cycle componentwise complementary  ...  A cpartite tournament is an orientation of a complete c-partite graph. Let V1, V2, . . . , Vc be the partite sets of D.  ...  Later, Guo and Volkmann [7] , [8] extended this result to locally semicomplete digraphs. In addition, there are some results on complementary cycles on bipartite tournaments by Z. Song, K.  ... 
doi:10.1007/978-3-540-72588-6_57 fatcat:mjgyzaoicrhspiqer5dnruvzdm

On cycles through two arcs in strong multipartite tournaments [article]

Alexandru I. Tomescu
2010 arXiv   pre-print
A multipartite tournament is an orientation of a complete c-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math.  ...  Lett. 20 (2007) 1148--1150], Volkmann proved that a strongly connected c-partite tournament with c > 3 contains an arc that belongs to a directed cycle of length m for every m ∈{3, 4, ..., c}.  ...  In [3] , Volkmann showed that a similar result holds for the case of strong multipartite tournaments.  ... 
arXiv:1006.0902v1 fatcat:n6vtmgdktzdnbftb7uwqwytx2a

Weakly quasi-Hamiltonian-set-connected multipartite tournaments

Yubao Guo, Mei Lu, Michel Surmacs
2012 Discrete Applied Mathematics  
In this paper, we characterize weakly quasi-Hamiltonian-set-connected multipartite tournaments which extends a result of Thomassen (1980) [6].  ...  A multipartite or c-partite tournament is an orientation of a complete c-partite graph.  ...  , as Lu and Guo did in [3] , we get the following definitions: A quasi-(k − 1)-path (quasik-cycle, respectively) in a multipartite tournament is a path (cycle, respectively) which contains vertices from  ... 
doi:10.1016/j.dam.2012.02.012 fatcat:l7halxtuhjg2ppdrng3n6sr5c4
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