On Round-Robin Tournaments with a Unique Maximum Score and Some Related Results
Date
2022-08-31Type of Work
18 pagesText
journal articles
preprints
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Richard Arnold Epstein (1927-2016) published the first edition of ”The Theory
of Gambling and Statistical Logic” in 1967. He introduced some material on roundrobin tournaments (complete oriented graphs) with n labeled vertices in Chapter 9;
in particular, he stated, without proof, that the probability that there is a unique
vertex with the maximum score tends to one as n tends to infinity. Our object here
is to give a proof of this result along with some historical remarks and comments.
We also give related results on pairs of equal scores and degrees in tournaments and
graphs.