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Each 3-strong tournament contains 3 vertices whose out-arcs are pancyclic. (English) Zbl 1207.05070
Summary: An arc in a tournament $$T$$ with $$n \geq 3$$ vertices is called pancyclic, if it is in a cycle of length $$k$$ for all $$3 \leq k \leq n$$. A. Yeo [“The number of pancyclic arcs in a k-strong tournament,” J. Graph Theory 50, No. 3, 212–219 (2005; Zbl 1081.05041)] proved that every 3-strong tournament contains two distinct vertices whose all out-arcs are pancyclic, and conjectured that each 2-strong tournament contains 3 such vertices. In this paper, we confirm Yeo’s conjecture for 3-strong tournaments.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles
##### Keywords:
tournament; out-arc; cycle; pancyclicity
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##### References:
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