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1 results

The Size of a Hypergraph and its Matching Number
HAO HUANG, PO-SHEN LOH, BENNY SUDAKOV
Journal:

Combinatorics, Probability and Computing / Volume 21 / Issue 3 / May 2012

Published online by Cambridge University Press:

20 January 2012, pp. 442-450
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More than forty years ago, Erdős conjectured that for any , every k-uniform hypergraph on n vertices without t disjoint 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.