The Number of Large Graphs with a Positive Density of Triangles
arXiv:math-ph/0203009 · doi:10.1023/A:1020489507547
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.
17 pages, 1 figure