### Abstract

For given k and s let n(k, s) be the largest cardinality of a set whose pairs can be covered by sk-sets. We determine n(k, q^{2} + q + 1) if a PG(2, q) exists, k > q(q + 1)^{2}, and the remainder of k divided by (q + 1) is at least √q. Asymptotic results are also given for n(k, s) whenever s is fixed and k → ∞. Our main tool is the theory of fractional matchings of hypergraphs.

Original language | English |
---|---|

Pages (from-to) | 248-271 |

Number of pages | 24 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 54 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1990 |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Covering pairs by q ^{2} + q + 1 sets.** / Füredi, Z.

Research output: Contribution to journal › Article

^{2}+ q + 1 sets',

*Journal of Combinatorial Theory, Series A*, vol. 54, no. 2, pp. 248-271. https://doi.org/10.1016/0097-3165(90)90034-T

}

TY - JOUR

T1 - Covering pairs by q2 + q + 1 sets

AU - Füredi, Z.

PY - 1990

Y1 - 1990

N2 - For given k and s let n(k, s) be the largest cardinality of a set whose pairs can be covered by sk-sets. We determine n(k, q2 + q + 1) if a PG(2, q) exists, k > q(q + 1)2, and the remainder of k divided by (q + 1) is at least √q. Asymptotic results are also given for n(k, s) whenever s is fixed and k → ∞. Our main tool is the theory of fractional matchings of hypergraphs.

AB - For given k and s let n(k, s) be the largest cardinality of a set whose pairs can be covered by sk-sets. We determine n(k, q2 + q + 1) if a PG(2, q) exists, k > q(q + 1)2, and the remainder of k divided by (q + 1) is at least √q. Asymptotic results are also given for n(k, s) whenever s is fixed and k → ∞. Our main tool is the theory of fractional matchings of hypergraphs.

UR - http://www.scopus.com/inward/record.url?scp=38249020520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249020520&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(90)90034-T

DO - 10.1016/0097-3165(90)90034-T

M3 - Article

AN - SCOPUS:38249020520

VL - 54

SP - 248

EP - 271

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -