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Article
Extending Partial Tournanents
Mathematical and Computer Modelling
  • LeRoy B. Beasley, Utah State University
  • David E. Brown, Utah State University
  • K. Brooks Reid
Document Type
Article
Publisher
Elsevier
Publication Date
1-1-2009
DOI
10.1016/j.mcm.2008.12.015
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) 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.
Citation Information
Beasley, L. B., D. E. Brown and K.B. Reid, Extending Partial Tournaments, Mathematical and Computer Modeling (2009) 50: 287 - 291.