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The Number of Large Graphs with a Positive Density of Triangles

Mathematical Physics 2015-06-26 v1 Combinatorics math.MP

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.

Keywords

Cite

@article{arxiv.math-ph/0203009,
  title  = {The Number of Large Graphs with a Positive Density of Triangles},
  author = {Pierre Collet and Jean-Pierre Eckmann},
  journal= {arXiv preprint arXiv:math-ph/0203009},
  year   = {2015}
}

Comments

17 pages, 1 figure