Each 3-strong Tournament Contains 3 Vertices Whose Out-arcs Are Pancyclic

Authors:
Jinfeng Feng
Affiliations:
RWTH Aachen University, Lehrstuhl C für Mathematik, 52056, Aachen, Germany
Venue:
Graphs and Combinatorics
Year:
2009

Citing 0
Cited 2

Out-arc pancyclicity of vertices in tournaments

Discrete Applied Mathematics
The structure of 4-strong tournaments containing exactly three out-arc pancyclic vertices

Journal of Graph Theory

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Abstract

An arc in a tournament T with n ≥ 3 vertices is called pancyclic, if it is in a cycle of length k for all 3 ≤ k ≤ n. Yeo (Journal of Graph Theory, 50 (2005), 212–219) 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.