The Turán number of disjoint copies of paths

The Turán number of a graph HH, denoted by ex(n,H)ex(n,H), is the maximum number of edges in a simple graph of order nn which does not contain HH as a subgraph. In this paper, we determine the value ex(n,k⋅P3) and characterize all extremal graphs for all positive integers nn and kk, where k⋅P3 is kk disjoint copies of a path on three vertices. This extends a result of Bushaw and Kettle (2011), which solved the conjecture proposed by Gorgol (2011).