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

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

2011-11-25

arxiv.org/abs/1111.6007v1

Mathematics

Combinatorics

Scientific paper

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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