Out-arc pancyclicity of vertices in tournaments

Authors:
Qiaoping Guo;Shengjia Li;Yubao Guo;Hongwei Li
Affiliations:
School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China and Institute of Mathematics and Applied Mathematics, Shanxi University, Taiyuan, 030006, China;Institute of Mathematics and Applied Mathematics, Shanxi University, Taiyuan, 030006, China;Lehrstuhl C für Mathematik, RWTH Aachen, Templergraben 55, 52062 Aachen, Germany;School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China and Institute of Mathematics and Applied Mathematics, Shanxi University, Taiyuan, 030006, China
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 5
Cited 0

Pancyclic out-arcs of a vertex in tournaments

Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Note: The number of vertices whose out-arcs are pancyclic in a 2-strong tournament

Discrete Applied Mathematics
The number of pancyclic arcs in a k-strong tournament

Journal of Graph Theory
Digraphs: Theory, Algorithms and Applications

Digraphs: Theory, Algorithms and Applications
Each 3-strong Tournament Contains 3 Vertices Whose Out-arcs Are Pancyclic

Graphs and Combinatorics

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Abstract

Yao, Guo and Zhang [T. Yao, Y. Guo, K. Zhang, Pancyclic out-arcs of a vertex in a tournament, Discrete Appl. Math. 99 (2000) 245-249.] 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. Yeo [A. Yeo, The number of pancyclic arcs in a k-strong tournament, J. Graph Theory 50 (2005) 212-219.] 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.