Intersecting families with covering number three

We consider k-graphs on n vertices, that is, F subset of(([n])(k)). A k-graph F is called intersecting if F boolean AND F 'not equal & empty; for all F,F 'is an element of F. In the present paper we prove that for k >= 7, n >= 2k, any intersecting k-graph F with covering number at least three, satisfies |F|<=((n-1)(k-1))-((n-k)(k-1))-((n-k-1)(k-1))+((n-2k)(k-1))+((n-k-2)(k-3))+3, the best possible upper bound which was proved in [4] subject to exponential constraints n>n(0)(k).