Mediated Digraphs and Quantum Nonlocality

Details Mediated Digraphs and Quantum Nonlocality Mediated Digraphs and Quantum Nonlocality

2004-11-30

arxiv.org/abs/math/0411653v2

Discrete Appl. Math. 150 (2005), no. 1-3, 41--50

Mathematics

Combinatorics

11 pages, 1 figure

Scientific paper

A digraph D=(V,A) is mediated if, for each pair x,y of distinct vertices of D, either xy belongs to A or yx belongs to A or there is a vertex z such that both xz,yz belong to A. For a digraph D, DELTA(D) is the maximum in-degree of a vertex in D. The "nth mediation number" mu(n) is the minimum of DELTA(D) over all mediated digraphs on n vertices. Mediated digraphs and mu(n) are of interest in the study of quantum nonlocality. We obtain a lower bound f(n) for mu(n) and determine infinite sequences of values of n for which mu(n)=f(n) and mu(n)>f(n), respectively. We derive upper bounds for mu(n) and prove that mu(n)=f(n)(1+o(1)). We conjecture that there is a constant c such that mu(n)=

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