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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