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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
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