Combinatorica

, Volume 33, Issue 5, pp 531–548 | Cite as

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

Original paper
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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.

Mathematics Subject Classification (2010)

Primary 05C38 Secondary 05C80, 05C81 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.A. Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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