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dc.contributor.authorMalinovsky, Yaakov
dc.contributor.authorMoon, John W.
dcterms.creatorhttps://orcid.org/0000-0003-2888-674Xen_US
dc.date.accessioned2022-10-13T14:32:15Z
dc.date.available2022-10-13T14:32:15Z
dc.date.issued2022-08-31
dc.description.abstractRichard 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.en_US
dc.description.sponsorshipWe thank Noga Alon for referring us to the work of Paul Erd˝os and Robin J. Wilson. We also thank Boris Alemi for executing the Maple program on a powerful computer and obtaining the data in the required format. The research of YM was supported by grant no. 2020063 from the United States–Israel Binational Science Foundation (BSF).en_US
dc.description.urihttps://arxiv.org/abs/2208.14932en_US
dc.format.extent18 pagesen_US
dc.genrejournal articlesen_US
dc.genrepreprintsen_US
dc.identifierdoi:10.13016/m2bdef-rdt9
dc.identifier.urihttps://doi.org/10.48550/arXiv.2208.14932
dc.identifier.urihttp://hdl.handle.net/11603/26168
dc.language.isoen_USen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis 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.en_US
dc.titleOn Round-Robin Tournaments with a Unique Maximum Score and Some Related Resultsen_US
dc.typeTexten_US


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