### Abstract

C(υ, k, 2) denotes the minimum number of k-subsets required to cover all pairs of a υ-set. Obviously, C(n^{2}+ n + 1, n + 1, 2) ≥n^{2}+ n + 1 where equality holds if and only if a finite projective plane exists. In this note the following conjecture of Mendelsohn is proved. If a PG(2, n) does not exist, then C(n^{2}+ n + 1)≥n^{2}+ n + 3.

Original language | English |
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Pages (from-to) | 321-324 |

Number of pages | 4 |

Journal | Discrete Mathematics |

Volume | 74 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1989 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**A projective plane is an outstanding 2-cover.** / Füredi, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 74, no. 3, pp. 321-324. https://doi.org/10.1016/0012-365X(89)90143-X

}

TY - JOUR

T1 - A projective plane is an outstanding 2-cover

AU - Füredi, Z.

PY - 1989

Y1 - 1989

N2 - C(υ, k, 2) denotes the minimum number of k-subsets required to cover all pairs of a υ-set. Obviously, C(n2+ n + 1, n + 1, 2) ≥n2+ n + 1 where equality holds if and only if a finite projective plane exists. In this note the following conjecture of Mendelsohn is proved. If a PG(2, n) does not exist, then C(n2+ n + 1)≥n2+ n + 3.

AB - C(υ, k, 2) denotes the minimum number of k-subsets required to cover all pairs of a υ-set. Obviously, C(n2+ n + 1, n + 1, 2) ≥n2+ n + 1 where equality holds if and only if a finite projective plane exists. In this note the following conjecture of Mendelsohn is proved. If a PG(2, n) does not exist, then C(n2+ n + 1)≥n2+ n + 3.

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UR - http://www.scopus.com/inward/citedby.url?scp=45249127003&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(89)90143-X

DO - 10.1016/0012-365X(89)90143-X

M3 - Article

VL - 74

SP - 321

EP - 324

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 3

ER -