Let G be an arbitrary graph. Then there is a set S and a family of subsets S_1, S_2, ... of S which can be put in one-to-one correspondence with the vertices of G in such a way that edges of G occur iff S_i !=S_j and S_i union S_j !=∅, where ∅ denotes the empty set. This theorem is attributed by Erdős et al. (1966) to Szpilrajn-Marczewski.

Erdős graph | intersection number