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A Problem on Tournaments

Published online by Cambridge University Press:  20 November 2018

P. Erdös  and
L. Moser
P. Erdös
Affiliation:
University of Alberta
L. Moser
Affiliation:
University of Alberta
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By a tournament we mean the outcome of a round-robin tournament in which there are no draws. Such a tournament may be represented by a graph in which the n players are represented by vertices labelled 1, 2, …, n, and the outcomes of the games are represented by directed edges so that every pair of vertices is joined by one directed edge. We call such a graph a complete directed graph. One can also represent such a tournament by an nXn matrix T=(tij) in which tij is 1 if i beats j, and 0 otherwise, so that T is a (0, 1) matrix with tij + tji = 1 for i≠j and (by definition) tii = 0.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964 , pp. 351 - 356
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Erdös, P., Mathematical Gazette, 47 (1963) pp. 220–223.Google Scholar