Kalai's conjecture in r-partite r-graphs

Kalai conjectured that every n-vertex r-uniform hypergraph with more than t-1 ( n ) edges contains all tight r-trees of some fixed r r-1 size t. We prove Kalai's conjecture for r-uniform hypergraphs that are r-partite. Our result is asymptotically best possible up to replacing the term t-1r with the term t-r+1 r . We apply our main result in graphs to show an upper bound for the Turan number of trees. (c) 2023 Published by Elsevier Ltd.