Note on forcing pairs

The notion of forcing pairs is located in the study of quasi-random graphs. Roughly speaking, a pair of graphs ( F , F ′ ) is called forcing if the following holds: suppose for a sequence of graphs ( G n ) there is a p > 0 such that the number of copies of F and the number of copies of F ′ in every graph G n of the sequence ( G n ) is approximately the same as the expected value in the random graph G ( n , p ) , then the sequence of graphs ( G n ) is quasi-random in the sense of Chung, Graham and Wilson. We describe a construction which, given any graph F with at least one edge, yields a graph F ′ such that ( F , F ′ ) forms a forcing pair.