Gutin, Gregory, Jones, N., Rafiey, A., Severini, S. and Yeo, Anders (2005) Mediated digraphs and quantum nonlocality. Discrete Applied Mathematics, 150 (1-3).
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A digraph D=(V,A) is mediated if for each pair x,y of distinct vertices of D, either xyA or yxA or there is a vertex z such that both xz,yzA. For a digraph D, Δ-(D) is the maximum in-degree of a vertex in D. The nth mediation number μ(n) is the minimum of Δ-(D) over all mediated digraphs on n vertices. Mediated digraphs and μ(n) are of interest in the study of quantum nonlocality. We obtain a lower bound f(n) for μ(n) and determine infinite sequences of values of n for which μ(n)=f(n) and μ(n)>f(n), respectively. We derive upper bounds for μ(n) and prove that μ(n)=f(n)(1+o(1)). We conjecture that there is a constant c such that μ(n)f(n)+c. Methods and results of design theory and number theory are used.
This is a Submitted version This version's date is: 2005 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/0007e1ba-c27f-af65-cb2d-744fdb106245/7/
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