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- W2043647572 abstract "A digraph D is cycle-connected if for every pair of vertices u,v∈V(D) there exists a directed cycle in D containing both u and v. In 1999, Ádám [A. Ádám, On some cyclic connectivity properties of directed graphs, Acta Cybernet. 14 (1) (1999) 1–12] posed the following problem. Let D be a cycle-connected digraph. Does there exist a universal arc in D, i.e., an arc e∈A(D) such that for every vertex w∈V(D) there is a directed cycle in D containing both e and w? A c-partite or multipartite tournament is an orientation of a complete c-partite graph. Recently, Hubenko [A. Hubenko, On a cyclic connectivity property of directed graphs, Discrete Math. 308 (2008) 1018–1024] proved that each cycle-connected bipartite tournament has a universal arc. As an extension of this result, we show in this note that each cycle-connected multipartite tournament has a universal arc." @default.
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- W2043647572 date "2009-03-01" @default.
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- W2043647572 title "Every cycle-connected multipartite tournament has a universal arc" @default.
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- W2043647572 doi "https://doi.org/10.1016/j.disc.2008.01.032" @default.
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