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Journal of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0894-0347-1994-1224593-5
MathSciNet review: 1224593
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Abstract: We prove a linear upper bound on the function $n(r) = {\text {min}}\{ \left | {\mathcal {H}} \right |:\mathcal {H}$ an $r$-uniform, intersecting hypergraph with $\tau (\mathcal {H}) = r\}$, thus settling a longstanding problem of Erdös and Lovász.


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Keywords: Hypergraphs, extremal problems, transversal designs
Article copyright: © Copyright 1994 American Mathematical Society