Article ID Journal Published Year Pages File Type
420369 Discrete Applied Mathematics 2010 10 Pages PDF
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 uu such that every out-arc of uu 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 kk-strong tournament, J. Graph Theory 50 (2005) 212–219.] conjectured that every 2-strong tournament has three distinct vertices {x,y,z}{x,y,z}, such that every arc out of x,yx,y and zz is pancyclic. In this paper, we also prove that Yeo’s conjecture is true.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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