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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

On a problem of Erdős and Lovász. II. $ n(r)=O(r)$


Author: Jeff Kahn
Journal: J. Amer. Math. Soc. 7 (1994), 125-143
MSC: Primary 05B40; Secondary 05C35, 05C65
MathSciNet review: 1224593
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Abstract: We prove a linear upper bound on the function $ n(r) = {\text{min}}\{ \left\vert {\mathcal{H}} \right\vert:\mathcal{H}$ an $ r$-uniform, intersecting hypergraph with $ \tau (\mathcal{H}) = r\} $, thus settling a longstanding problem of Erdös and Lovász.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0894-0347-1994-1224593-5
PII: S 0894-0347(1994)1224593-5
Keywords: Hypergraphs, extremal problems, transversal designs
Article copyright: © Copyright 1994 American Mathematical Society