Communication: Mediated digraphs and quantum nonlocality

  • Authors:

  • G. Gutin;N. Jones;A. Rafiey;S. Severini;A. Yeo

  • Affiliations:

  • Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Mathematics, Bristol University, University Walk, Bristol BS8 1TW, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Mathematics and Department of Computer Science, University of York, YO10 5DD, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2005

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Abstract

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