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Quadrangularity and Strong Quadrangularity in Tournaments

J. Richard Lundgren·K. B. Reid·Simone Severini·Dustin J. Stewart
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Abstract

The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. A directed graph is said to support M if its adjacency matrix is the pattern of M. If M is an orthogonal matrix, then a digraph which supports M must satisfy a condition known as quadrangularity. We look at quadrangularity in tournaments and determine for which orders quadrangular tournaments exist. We also look at a more restrictive necessary condition for a digraph to support an orthogonal matrix, and give a construction for tournaments which meet this condition.

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J. Richard Lundgren, K. B. Reid, Simone Severini, Dustin J. Stewart. 2004-09-24. Quadrangularity and Strong Quadrangularity in Tournaments. https://arxiv.org/abs/math/0409474

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