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The Size of a Hypergraph and its Matching Number

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journal contribution
posted on 01.09.2011, 00:00 authored by Hao Huang, Po-Shen Loh, Benny Sudakov

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.

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© Cambridge University Press

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01/09/2011

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