Cycles in multipartite tournaments: results and problems

Authors:
Lutz Volkmann
Affiliations:
Lehrstuhl II für Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany
Venue:
Discrete Mathematics
Year:
2002

Citing 44
Cited 4

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Graphs & digraphs (2nd ed.)
Locally semicomplete digraphs: a generalization of tournaments

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On multipartite tournaments

Journal of Combinatorial Theory Series B
On cycles in multipartite tournaments

Journal of Combinatorial Theory Series B
Complementary cycles of all lengths in tournaments

Journal of Combinatorial Theory Series B
In-tournament digraphs

Journal of Combinatorial Theory Series B
Pancyclic oriented graphs

Journal of Graph Theory
Complementary cycles containing a fixed arc in diregular bipartite tournaments

Discrete Mathematics
Cycles in multipartite tournaments

Journal of Combinatorial Theory Series B
Weakly Hamiltonian-connected vertices in bipartite tournaments

Journal of Combinatorial Theory Series B
On complementary cycles in locally semicomplete digraphs

Discrete Mathematics
Weakly Hamiltonian-connected ordinary multipartite tournaments

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

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Quasi-transitive digraphs

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Digraphs with the path-merging property

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Characterizations of vertex pancyclic and pancyclic ordinary complete multipartite digraphs

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Strongly Hamiltonian-connected locally semicomplete digraphs

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A complete solution of a problem of Bondy concerning multipartite tournaments

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Locally semicomplete digraphs that are complementary m-pancyclic

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Weakly Hamiltonian-connected locally semicomplete digraphs

Journal of Graph Theory
Long cycles in bipartite tournaments

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On k-strong and k-cyclic digraphs

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A sufficient condition for a semicomplete multipartite digraph to be Hamiltonian

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One-diregular subgraphs in semicomplete multipartite digraphs

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On cycles through a given vertex in multipartite tournaments

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Vertex deletion and cycles in multipartite tournaments

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Longest paths in semicomplete multipartite digraphs

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A polynomial time algorithm for finding a cycle covering a given set of vertices in a semicomplete multipartite digraph

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The ratio of the longest cycle and longest path on semicomplete mutlipartitite digraphs

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Pancyclic in-tournaments

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Almost all almost regular c-partite tournaments with c ≥ 5 are vertex pancyclic

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Pancyclic orderings of in-tournaments

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Tournament-like oriented graphs

Tournament-like oriented graphs
Generalizations of tournaments: A survey

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A polynomial algorithm for the Hamiltonian cycle problem in semicomplete multipartite digraphs

Journal of Graph Theory
A note on vertex pancyclic oriented graphs

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Hamilton cycles, avoiding prescribed arcs, in close-to-regular tournaments

Journal of Graph Theory
Diregular c-partite tournaments are vertex-pancyclic when c ≥ 5

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Vertex pancyclic in-tournaments

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On the connectivity of close to regular multipartite tournaments

Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Paths and cycles containing given arcs, in close to regular multipartite tournaments

Journal of Combinatorial Theory Series B
On the connectivity of close to regular multipartite tournaments

Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Complementary cycles in almost regular multipartite tournaments, where one cycle has length four

Discrete Applied Mathematics

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Abstract

A tournament is an orientation of a complete graph, and in general a multipartite tournament is an orientation of a complete n-partite graph. Many results about cycles in tournaments are known, but closely related problems involving cycles in multipartite tournaments have received little attention until recently. 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.