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Characterizations of vertex pancyclic and pancyclic ordinary complete multipartite digraphs

G. Gutin
1995 Discrete Mathematics  
Such a digraph D is called ordinary if for any pair X, Y of its partite sets the set of arcs with end vertices in We characterize all the pancyclic and vertex pancyclic ordinary complete multipartite digraphs  ...  A digraph obtained by replacing each edge of a complete multipartite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a complete multipartite digraph.  ...  As opposed to the characterization of even pancyclic bipartite graphs the last one cannot imply immediately a characterization of pancyclic (or vertex pancyclic) ordinary complete m-partite digraphs.  ... 
doi:10.1016/0012-365x(93)e0195-a fatcat:ldyc6pztufekha4x4sixvoptwu

Author index to volume 141 (1995)

1995 Discrete Mathematics  
., Characterizations of vertex pancyclic and pancyclic ordinary complete multipartite digraphs Hartsfield, N. and W.F. Smyth, A family of sparse graphs of large sum number Haussler. D., see E.  ...  Faudree Joseph, A., The isomorphism problem for Cayley digraphs on groups of prime-squared order Kayathri, K., see S.A. Choudum Knill, E., A. Ehrenfeucht and D.  ... 
doi:10.1016/0012-365x(95)90065-s fatcat:y6rzq6lsazb37fembgwosutzre

Cycles in multipartite tournaments: results and problems

Lutz Volkmann
2002 Discrete Mathematics  
A tournament is an orientation of a complete graph, and in general a multipartite tournament is an orientation of a complete n-partite graph.  ...  We describe some of the rapid progress in recent years on this topic, including powerful new methods and techniques. This study give rise to various interesting problems and conjectures.  ...  Acknowledgements I would like to thank my students Yubao Guo and Meike Tewes for fruitful discussions during a lot of years and many valuable detailed comments.  ... 
doi:10.1016/s0012-365x(01)00419-8 fatcat:rg3yfj4nazaj5afljiv4hbyrvq

Page 4071 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
Finally, the authors give a characterization of those ordinary multipartite tournaments that have a cycle through any set of k vertices.  ...  G is vertex pancyclic iff each vertex of G lies on a triangle.  ... 

Multipartite tournaments: A survey

Lutz Volkmann
2007 Discrete Mathematics  
A multipartite or c-partite tournament is an orientation of a complete c-partite graph.  ...  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.  ...  Acknowledgments I am grateful to my colleagues Gregory Gutin and Anders Yeo as well as to both of the anonymous referees for their useful remarks and suggestions.  ... 
doi:10.1016/j.disc.2007.03.053 fatcat:25sft4ap2zat5o3iocbum4w3zy

Page 1324 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
(IL-TLAV; Tel Aviv) Characterizations of vertex pancyclic and pancyclic ordinary complete multipartite digraphs. (English summary) Discrete Math. 141 (1995), no. 1-3, 153-162.  ...  Some necessary and sufficient conditions for an ordinary semicomplete multipartite digraph to have the pan- cyclic and vertex-pancyclic properties are obtained in this paper.  ... 

Vertex-Pancyclism in the Generalized Sum of Digraphs [article]

N. Cordero-Michel, H. Galeana-Sánchez
2020 arXiv   pre-print
A digraph D=(V(D), A(D)) of order n≥ 3 is pancyclic, whenever D contains a directed cycle of length k for each k∈{3,...,n}; and D is vertex-pancyclic iff, for each vertex v∈ V(D) and each k∈{3,...  ...  ., D_k be a collection of k pairwise vertex disjoint Hamiltonian digraphs, in this paper we give simple sufficient conditions for a digraph D∈⊕_i=1^k D_i be vertex-pancyclic.  ...  In [7] , Gutin characterized pancyclic and vertex-pancyclic ordinary complete k-partite digraphs: Theorem 1 (Gutin [7] ). (1) An ordinary complete k-partite digraph (k ≥ 3) D is pancyclic if and only  ... 
arXiv:2011.01886v1 fatcat:jytmfjn57raejpx3i4ewccxr2a

Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey

G. Gutin
1995 Journal of Graph Theory  
A digraph obtained by replacing each edge of a complete m-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete m-partite digraph.  ...  We describe results (theorems and algorithms) on directed walks in semicomplete m-partite digraphs including some recent results concerning tournaments.  ...  3) digraph D is pancyclic (vertex pancyclic).  ... 
doi:10.1002/jgt.3190190405 fatcat:7cnx4wtlobhcnjizv3ry7lnszi

Page 3168 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
of regular ordinary multipartite tournaments.  ...  A partial m-cycle system of order n is a pair (X, P) where X is the vertex set of a complete graph K,, and P is a collection of edge- disjoint m-cycles from (some of) the edges in K,.  ... 

Page 7697 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
An in-tournament D of order n is said to be vertex k-pancyclic if, for every vertex v € V(D) and for every integer p with k < p <n, the vertex v is contained in a cycle of length p.  ...  We define a digraph to be nearly acyclic if it is obtained from an acyclic digraph by substituting a (directed) triangle or a single vertex for each vertex of the acyclic digraph.  ... 

A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs [article]

Samvel Kh. Darbinyan, Iskandar A. Karapetyan
2017 arXiv   pre-print
{x,y} dominates a vertex z if x→ z and y→ z; in this case, we call the pair {x,y} dominating.  ...  In this paper we prove: If max{d(x), d(y)}≥ 2a-2 for every dominating pair of vertices {x,y}, then D contains cycles of all lengths 2,4, ... , 2a-2 or D is isomorphic to a certain digraph of order ten  ...  A characterization of pancyclic ordinary k-partite (k ≥ 3) tournaments (respectively, pancyclic ordinary complete multipartite digraphs) was established in [18] (respectively, in [19] ).  ... 
arXiv:1706.00233v1 fatcat:uafwlvxlirhjhpkylscsjbuila

Page 148 of Mathematical Reviews Vol. 28, Issue Index [page]

Mathematical Reviews  
Characterizations of vertex pancyclic and pancyclic ordinary complete multipartite digraphs.  ...  (English summary) 96c:05076 — Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey.  ... 

Subject Index Volumes 1–200

2001 Discrete Mathematics  
Erdös and Sós, 4925 Erdös and Szekeres, 4879 Erdös et al., 5529, 5888 Erdös Rubin Taylor, 3815 Erdös Sós Turán, 506 Everett, 2901 Faigle and Sands, 2122 Faudree et al., 4399 Faudree Gould Jacobson  ...  Slater, 5299 Hertz and de Werra, 3748 Hibi, 4839 Hoàng, 3748, 4811 Holton, 1660 Holyer and Cockayne, 1118 Howorka, 2636  ...  , see end vertex n, q), 1738 a complete graph, 5689 a digraph, 5279 embedding of a finite linear space, 2225 poset, 376 embedding of a graph, 452, 1338, 2436, 2611, 3920, 5758 in a book, 5585  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

Page 176 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
(English summary) 2000k:05163 Pan, Lingiang (with Zhou, Guofei; Zhang, Ke Min') A note on arc pancyclicity of regular ordinary multipartite tournaments.  ...  (English and Chinese summaries) 2000i:05104 Guo, Yubao Outpaths in semicomplete multipartite digraphs. (English summary) 2000¢:05096 COMBINATORICS 2000 Hammack, Richard H.  ... 

Page 1504 of Mathematical Reviews Vol. 28, Issue Index [page]

Mathematical Reviews  
Characterizations of vertex pancyclic and pancyclic ordinary complete multipartite digraphs.  ...  (English summary) 96¢:05076 — Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey.  ... 
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