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


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.

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Correspondence to Viktor Harangi.

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Harangi, V. On the density of triangles and squares in regular finite and unimodular random graphs. Combinatorica 33, 531–548 (2013). https://doi.org/10.1007/s00493-013-2907-0

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Mathematics Subject Classification (2010)

  • Primary 05C38
  • Secondary 05C80, 05C81