An application of the Ramsey theorem to ordered r-tournaments
type: Item
instance of: scholarly article
title: An application of the Ramsey theorem to ordered r-tournaments
zbMATH Open document ID: 0595.05053
DOI: 10.1016/0012-365X(86)90105-6
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: An r-tournament consists of a linearly ordered n-set V and a linear ordering of each of its r-element subsets. The r-tournament is transitive (anti-transitive) if the order of each of its r-element subsets agrees with the ordering of V (agrees with the reverse of the ordering of V). Given an r-tournament with underlying set V and a subset U of V, the r- tournament on U, which assigns the induced order to U and assigns to any r-subset the order it was given as a subset of V, is called an r- subtournament. The main result of this paper is: Theorem. For every two positive integers r and n satisfying \(r\leq n\), there exists a positive integer f(r,n) with the following property: Every ordered r-tournament on f(r,n) vertices either contains a transitive r-subtournament on n vertices or an anti-transitive r-tournament on n vertices.
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 3957161
zbMATH Keywords: ordered r-tournament
zbMATH Keywords: transitive r-subtournament
zbMATH Keywords: anti-transitive r- tournament
author: Arie Bialostocki
reviewed by: Jack E. Graver
MaRDI profile type: Publication
cites work: Disproof of a conjecture of Erdös and moser on tournaments
cites work: The Voting Problem
full work available at URL: 0012-365x(86)90105-6
OpenAlex ID: W2071283792
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description: scientific article; zbMATH DE number 3957161