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Out-arc pancyclicity of vertices in tournaments. (English) Zbl 1220.05049
Summary: T. Yao, Y. Guo and K. Zhang [“Pancyclic out-arcs of a vertex in a tournament,” Discrete Appl. Math. 99, No. 1-3, 245–249 (2000; Zbl 0939.05045)] proved that every strong tournament contains a vertex $$u$$ such that every out-arc of $$u$$ is pancyclic. In this paper, we prove that every strong tournament with minimum out-degree at least two contains two such vertices. A. Yeo [“The number of pancyclic arcs in a $$k$$-strong tournament,” J. Graph Theory 50, No. 3, 212–219 (2005; Zbl 1081.05041)] conjectured that every 2-strong tournament has three distinct vertices $$\{ x,y,z \}$$, such that every arc out of $$x,y$$ and $$z$$ is pancyclic. In this paper, we also prove that Yeo’s conjecture is true.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles
##### Keywords:
tournaments; cycles; out-arcs; pancyclicity
Full Text:
##### References:
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