Quasi-randomness and the distribution of copies of a fixed graph

@article{Shapira2008QuasirandomnessAT,
  title={Quasi-randomness and the distribution of copies of a fixed graph},
  author={Asaf Shapira},
  journal={Combinatorica},
  year={2008},
  volume={28},
  pages={735-745}
}
  • A. Shapira
  • Published 1 November 2008
  • Mathematics
  • Combinatorica
We show that if a graph G has the property that all subsets of vertices of size n/4 contain the “correct” number of triangles one would expect to find in a random graph G(n, 1/2), then G behaves like a random graph, that is, it is quasi-random in the sense of Chung, Graham, and Wilson [6]. This answers positively an open problem of Simonovits and Sós [10], who showed that in order to deduce that G is quasi-random one needs to assume that all sets of vertices have the correct number of triangles… 
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