Linear trees in uniform hypergraphs

Given a tree T on v vertices and an integer k ≥ 2 one can define the k -expansion T ( k ) as a k -uniform linear hypergraph by enlarging each edge with a new, distinct set of k − 2 vertices. T ( k ) has v + ( v − 1 ) ( k − 2 ) vertices. The aim of this paper is to show that using the delta-system method one can easily determine asymptotically the size of the largest T ( k ) -free n -vertex hypergraph, i.e., the Turán number of T ( k ) .