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Quadrangularity and Strong Quadrangularity in Tournaments

Lundgren, JR; Reid, KB; Severini, S; Stewart, DJ; Quadrangularity and Strong Quadrangularity in Tournaments. Australasian Journal of Combinatorics , 34 247-.

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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.

Type: Article
Title: Quadrangularity and Strong Quadrangularity in Tournaments
Additional information: 12 pages
Keywords: math.CO, math.CO, quant-ph, 05C20; 05C50; 05C75
URI: http://discovery.ucl.ac.uk/id/eprint/404753
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