For a graph $G$ let $\tau (G)$ denote the minimal number of vertices that include at least one from each maximal clique of $G$ on at least two vertices (sometimes called the clique transversal number).Let $H(n)$ be maximal such that every triangle-free graph on $n$ vertices contains an independent set on $H(n)$ vertices.If $G$ is a graph on $n$ vertices then is$$\tau (G)\le n-H(n)?$$