KöMaL 2016 B4763

Let $G$ be a simple undirected graph of $n$ vertices. Prove that it is possible to assign infinite sets $\mathcal{H}_1,\mathcal{H}_2, \dots, \mathcal{H}_n$ of natural numbers to the graph such that the intersection of two sets is infinite if the corresponding vertices are joined by an edge, and empty if there is no edge joining the vertices.