Extending Partial Tournaments
Document Type
Article
Journal/Book Title/Conference
Mathematical and Computer Modelling
Volume
50
Issue
1
Publisher
Elsevier
Publication Date
2009
First Page
287
Last Page
291
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.
Recommended Citation
Beasley, L. B., D. E. Brown and K.B. Reid, Extending Partial Tournaments, Mathematical and Computer Modeling (2009) 50: 287 - 291.
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