Balanced tournament designs and related topics
type: Item
instance of: scholarly article
title: Balanced tournament designs and related topics
zbMATH Open document ID: 0682.05013
DOI: 10.1016/0012-365X(89)90358-0
author: Scott A. Vanstone
author: Esther R. Lamken
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: This is an excellent review paper on the topic of Balanced Tournament Designs. A balanced tournament design of order n, BTD(n), is an \(n\times (2n-1)\) array defined on a set of 2n elements V such that (1) each cell of the array contains a pair of distinct elements from V, (2) every pair of distinct elements from V is contained in some cell, (3) each element is contained in each column, and (4) no element is contained in more than 2 cells of each row. As is well known by now, the existence of such designs has been completely settled. All the crucial theorems are reviewed and various extensions and generalizations are presented. Close connections with other combinatorial systems are also pointed out, such as Room squares, Kotzig factorizations in graph theory, resolvable balanced incomplete block designs, Kirkman squares, etc. All in all, highly recommended reading for researchers in combinatorial designs.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 4116544
zbMATH Keywords: round robin tournaments
zbMATH Keywords: room square design
zbMATH Keywords: resolvable BIBD
zbMATH Keywords: Balanced Tournament Designs
zbMATH Keywords: BTD
reviewed by: B. Leo Raktoe
MaRDI profile type: Publication
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full work available at URL: 0012-365x(89)90358-0
OpenAlex ID: W2006974614
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description: scientific article; zbMATH DE number 4116544