On the Turán number of forests

Abstract

The Tuŕan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Tuŕan number and find the unique extremal graph for forests consisting of paths when n is sufficiently large. This generalizes a result of Bushaw and Kettle [Combinatorics, Probability and Computing 20:837-853, 2011]. We also determine the Tuŕan number and extremal graphs for forests consisting of stars of arbitrary order.