Quadrangularity in Tournaments

Lundgren, J. Richard; Severini, Simone; Stewart, Dustin J.

Quadrangularity in Tournaments

Authors

Lundgren, J. Richard

Severini, Simone

Stewart, Dustin J.

Description

The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be orthogonal is a property known as combinatorial orthogonality. If the adjacency matrix of a directed graph forms a pattern of a combinatorially orthogonal matrix, we say the digraph is quadrangular. We look at the quadrangular property in tournaments and regular tournaments.
13 pages