The Asymmetry Number of Finite Tournaments, and Some Related Results

Satake, Shohei
November 2017
Graphs & Combinatorics;Nov2017, Vol. 33 Issue 6, p1433
Academic Journal
We introduce the concept of asymmetry number for finite tournaments, as a natural generalization of that for graphs by Erdős and Rényi (Acta Math Acad Sci Hungar 14:295-315, 1963). We prove an upper bound for the asymmetry number of finite tournaments and discuss its asymptotically best possibility. We also give an alternative proof of a theorem by Jaligot and Khelif (Aequat Math 67:73-79, 2004) which states that the random tournament can be expressed by a Cayley tournament on an arbitrary countable group without involutions. We slightly improve a result by Cameron and Johnson (Math Proc Camb Philos Soc 102:223-231, 1987).


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