On Round-Robin Tournaments with a Unique Maximum Score and Some Related Results

Thumbnail Image

Files

2208.14932.pdf (217.46 KB)

Links to Files

https://arxiv.org/abs/2208.14932

Permanent Link

https://doi.org/10.48550/arXiv.2208.14932
 http://hdl.handle.net/11603/26168

Collections

UMBC Mathematics and Statistics Department
UMBC Faculty Collection

Author/Creator

Author/Creator ORCID

https://orcid.org/0000-0003-2888-674X

Date

2022-08-31

Type of Work

journal articles
preprints
Text

Department

Program

Citation of Original Publication

Rights

This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.

Subjects

Abstract

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.