Quadrangularity and Strong Quadrangularity in Tournaments
J. Richard Lundgren, K. B. Reid, Simone Severini, Dustin J. Stewart · Australas. J Comb. · 2004
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.