A conjecture on triangles of graphs (Q2276982)

The author conjectured in 1981: If a grah G does not contain more than k pairwise edge-disjoint triangles, then there exists a set of at most 2k edges that meets all triangles of G. In the paper this conjecture is proved for various classes of graphs (planar graphs, graphs with n vertices and at least \((7/16)n^ 2\) edges, chordal graphs without a complete subgraph on 5 vertices). Related results for 3-uniform hypergraphs and digraphs as well as weaker and stronger versions of the conjecture for special classes of graphs are discussed. Open problems are presented.