  In 1982, Tuza conjectured that the size $\tau(G)$ of a minimum set of edges
that intersects every triangle of a graph $G$ is at most twice the size
$\nu(G)$ of a maximum set of edge-disjoint triangles of $G$. This conjecture
was proved for several graph classes. In this paper, we present three results
regarding Tuza's Conjecture for dense graphs. By using a probabilistic
argument, Tuza proved its conjecture for graphs on $n$ vertices with minimum
degree at least $\frac{7n}{8}$. We extend this technique to show that Tuza's
conjecture is valid for split graphs with minimum degree at least
$\frac{3n}{5}$; and that $\tau(G) < \frac{28}{15}\nu(G)$ for every tripartite
graph with minimum degree more than $\frac{33n}{56}$. Finally, we show that
$\tau(G)\leq \frac{3}{2}\nu(G)$ when $G$ is a complete 4-partite graph.
Moreover, this bound is tight.
