A proof for a conjecture of Gorgol

The Turán numberex(n,H) is the maximum number of edges in a graph on n vertices which does not contain H as a subgraph. Gorgol gives a lower bound for ex(n,H) when H is the disjoint union of k copies of P3 and conjectures this bound is tight. In this paper, we give an algorithmic proof of Gorgol's Conjecture.