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Quasi-randomness is determined by the distribution of copies of a fixed graph in equicardinal large sets. (English) Zbl 1224.05476
A graph $$G(n)$$ is $$p$$-quasi-random if it behaves like the random graph $$G(n,p)$$ for sufficiently large $$n$$ and any $$0<p<1$$. It is proved that $$G(n)$$ is $$p$$-quasi-random if, for every fixed graph $$H$$ and every fixed proportion $$0<w<1$$, the subgraph of $$G(n)$$ induced by any vertex subset of size $$wn$$ contains as many copies of $$H$$ as would be expected in $$G(n,p)$$.

##### MSC:
 05C80 Random graphs (graph-theoretic aspects)
##### Keywords:
random graph; pseudo-randomness; quasi-randomness
Full Text:
##### References:
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