Quadrangularity and Strong Quadrangularity in Tournaments
Combinatorics
2007-05-23 v1 Quantum Physics
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.
Cite
@article{arxiv.math/0409474,
title = {Quadrangularity and Strong Quadrangularity in Tournaments},
author = {J. Richard Lundgren and K. B. Reid and Simone Severini and Dustin J. Stewart},
journal= {arXiv preprint arXiv:math/0409474},
year = {2007}
}
Comments
12 pages