Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey
Journal of Graph Theory
One-diregular subgraphs in semicomplete multipartite digraphs
Journal of Graph Theory
Almost all almost regular c-partite tournaments with c ≥ 5 are vertex pancyclic
Discrete Mathematics
Cycles in multipartite tournaments: results and problems
Discrete Mathematics
Diregular c-partite tournaments are vertex-pancyclic when c ≥ 5
Journal of Graph Theory
Pancyclic out-arcs of a vertex in oriented graphs
Information Processing Letters
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The global irregularity of a digraph D is defined by i"g(D)=max{d^+(x),d^-(x)}-min{d^+(y),d^-(y)} over all vertices x and y of D (including x=y). In this paper we prove that if D is a c-partite tournament such that c=4 and |V(D)|476i"g(D)+13917 then there exists a path of length l between any two given vertices for all 42==4 have a Hamilton cycle through any given arc, and the condition c=4 is best possible. Sufficient conditions are furthermore given for when a c-partite tournament with c=4 has a Hamilton cycle containing a given path or a set of given arcs. We show that all sufficiently large c-partite tournaments with c=5 and bounded i"g are vertex-pancyclic and all sufficiently large regular 4-partite tournaments are vertex-pancyclic. Finally we give a lower bound on the number of Hamilton cycles in a c-partite tournament with c=4.