On a conjecture of Tuza about packing and covering of triangles

Zs. Tuza conjectured that if a simple graph G does not contain more than k pairwise edge disjoint triangles, then there exists a set of at most 2k edges which meets all triangles in G. We prove this conjecture for K3, 3-free graphs (graphs that do not contain a homeomorph of K3, 3). Two fractional versions of the conjecture are also proved.