On the number of K₄-saturating edges

Let G be a K₄-free graph; an edge in its complement is a K₄-saturating edge if the addition of this edge to G creates a copy of K₄. Erdos and Tuza conjectured that for any n-vertex K₄-free graph G with ⌊n²/4⌋+1 edges, one can find at least (1+o(1))n216 K₄-saturating edges. We construct a graph with only 2n233 K₄-saturating edges. Furthermore, we prove that it is best possible, i.e., one can always find at least (1+o(1))2n233 K₄-saturating edges in an n-vertex K₄-free graph with ⌊n²/4⌋+1 edges.