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On a conjecture of Brualdi and Shen on block transitive tournaments

✍ Scribed by P. Acosta; A. Bassa; A. Chaikin; A. Riehl; A. Tingstad; L. Zhao; D. J. Kleitman

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
167 KB
Volume
44
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

The following conjecture of Brualdi and Shen is proven in this paper: let n be partitioned into natural numbers no one of which is greater than (n + 1) / 2. Then, given any sequence of wins for the players of some tournament among n players, there is a partition of the players into blocks with cardinalities given by those numbers, and a tournament with the given sequence of wins, that is transitive on the players within each block. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 215–230, 2003

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