The Number of Large Graphs with a Positive Density of Triangles |
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| Authors: | P. Collet J.-P. Eckmann |
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| Affiliation: | (1) Centre de Physique Théorique, Laboratoire CNRS UMR 7644, École Polytechnique, F-91128 Palaiseau Cedex, France;(2) Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland;(3) Section de Mathématiques, Université de Genève, CH-1211 Genève 4, Switzerland |
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| Abstract: | We give upper and lower bounds on the number of graphs of fixed degree which have a positive density of triangles. In particular, we show that there are very few such graphs, when compared to the number of graphs without this restriction. We also show that in this case the triangles seem to cluster even at low density. |
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| Keywords: | Random graphs very large deviations world-wide-web |
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