Quasi-random graphs

@article{Graham1989QuasirandomG,
  title={Quasi-random graphs},
  author={Fan Chung Graham and Ronald L. Graham and Richard M. Wilson},
  journal={Combinatorica},
  year={1989},
  volume={9},
  pages={345-362}
}
We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class. 
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References

SHOWING 1-10 OF 23 REFERENCES
Quasi-Random Hypergraphs
TLDR
A large equivalence class of properties shared by most hypergraphs, including so-called random hyper graphs, are described, which shows that many global properties of hyperGraphs are actually consequences of simple local conditions.
Pseudo-Random Graphs
Explicit construction of linear sized tolerant networks
Intersection theorems with geometric consequences
TLDR
It is proved that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℽ there is one set within which all the distances are realised.
A Constructive Solution to a Tournament Problem
By a tournament Tn on n vertices, we shall mean a directed graph on n vertices for which every pair of distinct vertices form the endpoints of exactly one directed edge (e.g., see [5]). If x and y
Topics in Multiplicative Number Theory
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value
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