The number of vertices whose out-arcs are pancyclic in a 2-strong tournament |
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Authors: | Ruijuan Li Shengjia Li Jinfeng Feng |
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Institution: | a School of Mathematical Sciences, Shanxi University, 030006 Taiyuan, PR China b Lehrstuhl C für Mathematik, RWTH Aachen University, 52056 Aachen, Germany |
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Abstract: | An arc going out from a vertex x in a digraph is called an out-arc of x. Yao et al. Discrete Appl. Math. 99 (2000) 245-249] proved that every strong tournament contains a vertex x such that all out-arcs of x are pancyclic. Recently, Yeo J. Graph Theory 50 (2005) 212-219] proved that each 3-strong tournament contains two such vertices. In this paper, we confirm that Yeo's result is also true for 2-strong tournaments. Our proof implies a polynomial algorithm to find two such vertices. |
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Keywords: | Tournaments Cycles Pancyclicity |
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