Before revision:  We prove that the number of 3-sized hyperedges is bounded by O  (n^2) and that this bound is tight. In addition, we show that the total number of hyperedges is  O(n^3)  .
After revision:  We prove that the number of 3-sized hyperedges is bounded by O (n^2) and that the total number of hyperedges is O(n^3) .