On a problem of Erdős and Lovász: Random lines in a projective plane

Jeff Kahn

doi:10.1007/BF01305234

On a problem of Erdős and Lovász: Random lines in a projective plane

Jeff Kahn

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

Theorem: There is a constant A such that if H is a random set of m ≥Aklog k lines from ℝ_k then P_r(τH<)→0(k→∞). Corollary: If there exists a ℝ_k then n(k)=O(klogk). These statements were conjectured by P. Erdo{combining double acute accent}s and L. Lovász in 1973. Let n(k) be the least size of an intersecting family of k-sets with cover number k, and let ℝ_k denote any projective plane of order k-1.

Original language	English (US)
Pages (from-to)	417-423
Number of pages	7
Journal	Combinatorica
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/BF01305234
State	Published - Dec 1992

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

Keywords

AMS subject classification code 1991: 05B40, 05C65, 05D05, 51E15

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10.1007/BF01305234

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AB - Theorem: There is a constant A such that if H is a random set of m ≥Aklog k lines from ℝk then Pr(τH<)→0(k→∞). Corollary: If there exists a ℝk then n(k)=O(klogk). These statements were conjectured by P. Erdo{combining double acute accent}s and L. Lovász in 1973. Let n(k) be the least size of an intersecting family of k-sets with cover number k, and let ℝk denote any projective plane of order k-1.

KW - AMS subject classification code 1991: 05B40, 05C65, 05D05, 51E15

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ER -

On a problem of Erdős and Lovász: Random lines in a projective plane

Abstract

All Science Journal Classification (ASJC) codes

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