%0 Journal Article %T On the number of edge-disjoint triangles in $K_4$-free graphs %A Ervin Gy£¿ri %A Bal¨¢zs Keszegh %J Mathematics %D 2015 %I arXiv %X We show the quarter of a century old conjecture that every $K_4$-free graph with $n$ vertices and $\lfloor n^2/4 \rfloor +k$ edges contains $k$ pairwise edge disjoint triangles. %U http://arxiv.org/abs/1506.03306v1