On the density of triangles and squares in regular finite and unimodular random graphs
- 79 Downloads
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
Unable to display preview. Download preview PDF.
- M. Abért, Y. Glasner and B. Virág: The measurable Kesten theorem, Preprint, 2011. arXiv:1111.2080.Google Scholar
- B. Bollobás: Extremal graph theory Dover Books on Mathematics, Dover Publications, 2004.Google Scholar
- P. Erdős and H. Sachs: Regul are Graphen gegebener Taillenweite mit minimaler Knotenzahl, Wiss. Z. Univ. Halle, Math.-Nat. 12 (1963), 251–258.Google Scholar
- H. Hatami, J. Hladký, D. Král’, S. Norine and A. Razborov: On the number of pentagons in triangle-free graphs, Preprint, 2011. arXiv:1102.1634v2.Google Scholar