 
Summary: Extending Partial Tournaments
LeRoy B. Beasley and David E. Brown
Department of Mathematics and Statistics, Utah State University
Logan, Utah 843224125, USA
Email: lbeasley@math.usu.edu; brown@math.usu.edu
K. Brooks Reid
Department of Mathematics, California State University San Marcos,
San Marcos, CA 92096
Email: breid@csusm.edu
Abstract
Let A be a (0, 1, )matrix with main diagonal all 0's and such that if ai,j = 1 or
then aj,i = or 0. Under what conditions on the row sums, and or column sums,
of A is it possible to change the 's to 0's or 1's and obtain a tournament matrix
(the adjacency matrix of a tournament digraph) with a specified score sequence?
We answer this question in the case of regular and nearly regular tournaments. The
result we give is best possible in the sense that no relaxation of any condition will
always yield a matrix that can be so extended.
2000 Mathematics Subject Classification : 15A45, 15A33, 15A03.
Key words and phrases : tournament digraph, tournament matrix, matrix completions
