Triangle packing and covering in dense random graphs

Given a simple graph G = (V, E), a subset of E is called a triangle cover if it intersects each triangle of G. Let nu(t) (G) and tau(t) (G) denote the maximum number of pairwise edge-disjoint triangles in G and the minimum cardinality of a triangle cover of G, respectively. Tuza (in: Finite and infinite sets, proceedings of Colloquia Mathematica Societatis, Janos Bolyai, p 888,1981) conjectured in 1981 that tau(t) (G)/nu(t) (G) <= 2 holds for every graph G. In this paper, we consider Tuza's Conjecture on dense random graphs. Under g(n, p) model with a constant p, we prove that the ratio of tau(t) (G) and nu(t) (G) has the upper bound close to 1.5 with high probability. Furthermore, the ratio 1.5 is nearly the best result when p >= 0.791. In some sense, on dense random graphs, these conclusions verify Tuza's Conjecture.