Edge-disjoint triangle conjecture for K4-free graphs

Let $G$ be a $K_4$-free graph on $n$ vertices with $t_2(n)+m$ edges, where $t_2(n)=\lfloor n^2/4\rfloor$ is the number of edges in the $2$-partite Turán graph on $n$ vertices. Edge-disjoint triangle conjecture. $G$ contains at least $m$ pairwise edge-disjoint triangles. The conjecture is presented as a longstanding problem and is the claim addressed by the paper; the supplied source does not state its resolution explicitly.