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More than forty years ago, Erdős conjectured that for any , every k-uniform hypergraph on n vertices without tdisjoint edges has at most max edges. Although this appears to be a basic instance of the hypergraph Turán problem (with a t-edge matching as the excluded hypergraph), progress on this question has remained elusive. In this paper, we verify this conjecture for all . This improves upon the best previously known range , which dates back to the 1970s.doi:10.1184/r1/6479984.v1 fatcat:zh5oqu2csba43kgzhtqrtqtvaa