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

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 S

• Type: Journal
• Year: 2008
• Where: COMBINATORICA
• Authors: Asaf Shapira
• Keywords: COMBINATORICA 2008, Open Problem, Random Graph, Triangle