On the density of triangles and squares in regular finite and unimodular random graphs

  • Authors:

  • Viktor Harangi

  • Affiliations:

  • A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary H-1364

  • Venue:
  • Combinatorica
  • Year:
  • 2013

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Abstract

We explicitly describe the possible pairs of triangle and square densities for r-regular finite simple graphs. We also prove that every r-regular unimodular random graph can be approximated by r-regular finite graphs with respect to these densities. As a corollary one gets an explicit description of the possible pairs of the third and fourth moments of the spectral measure of r-regular unimodular random graphs.