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The Size of a Hypergraph and its Matching Number

Published online by Cambridge University Press:  20 January 2012

HAO HUANG ,
PO-SHEN LOH  and
BENNY SUDAKOV
HAO HUANG
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail: huanghao@math.ucla.edu, bsudakov@math.ucla.edu)
PO-SHEN LOH
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: ploh@cmu.edu)
BENNY SUDAKOV
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail: huanghao@math.ucla.edu, bsudakov@math.ucla.edu)
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Abstract

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.

Keywords

Primary 05D1505C65
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 3 , May 2012 , pp. 442 - 450
Copyright
Copyright © Cambridge University Press 2012

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