Date of Award:

2002

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Advisor/Chair:

LeRoy B. Beasley

Abstract

The results of a round robin tournament can be represented as a matrix of zeros and ones, by ordering the players and placing a one in the (i,j) position if player i beat player j, and zeros otherwise. These matrices, called tournament matrices, can be represented by graphs, called tournament graphs. They have been the subject of much research and study, yet there have been few attempts to give a wide exposition on the subject. Those that have been done tend to focus on the graph theoretical aspects of tournaments. S. Ree and Y. Koh did write a brief survey from the matrix viewpoint in 1998, but it was not complete and not published.

This paper is an attempt to give an exposition on tournament matrices. Recent research will be presented, some new ideas and properties will be proposed, and a few applications of the material will be reviewed.

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