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

2011/11/25 by Viktor Harangi, Harangi, Viktor · 1 citation
Mathematics · #05C81 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05C38. Secondary 05C80 #math.CO #msc:05C38. #msc:05C80 #msc:05C81

paper · pdf · doi:10.48550/arxiv.1111.6007

arxiv created 2011/11/25 · arxiv updated 2011/11/28

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.

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