On a conjecture of Brualdi and Shen on block transitive tournaments | Zendy

Acosta P. | Zendy; Bassa A. | Zendy; Chaikin A. | Zendy; Riehl A. | Zendy; Tingstad A. | Zendy; Zhao L. | Zendy; Kleitman D. J. | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

On a conjecture of Brualdi and Shen on block transitive tournaments

Author(s) -

Acosta P.,

Bassa A.,

Chaikin A.,

Riehl A.,

Tingstad A.,

Zhao L.,

Kleitman D. J.

Publication year - 2003

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.10143

Subject(s) - tournament , conjecture , combinatorics , transitive relation , mathematics , partition (number theory) , sequence (biology) , block (permutation group theory) , graph , discrete mathematics , biology , genetics

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

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research