A Proof for a Conjecture of Gorgol

The Turán number of a graph H, ex(n,H), is the maximum number of edges in any graph on n vertices which does not contain H as a subgraph. Let P3 denote a path on 3 vertices, and kP3 denote k vertex-disjoint copies of P3. We determine ex(n,kP3) for all n and k proving a conjecture of Gorgol.