Date of Original Version

9-2011

Type

Article

Rights Management

© Cambridge University Press

Abstract or Description

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

10.1017/S096354831100068X

Included in

Mathematics Commons

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Published In

Combinatorics, Probability and Computing, 21, 3, 422-450.