A projective plane is an outstanding 2-cover

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)321-324
Number of pages4
JournalDiscrete Mathematics
Volume74
Issue number3
DOIs
Publication statusPublished - 1989

Fingerprint

Finite projective plane
Projective plane
Equality
Cover
If and only if
Denote
Subset

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

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

In: Discrete Mathematics, Vol. 74, No. 3, 1989, p. 321-324.

Research output: Contribution to journalArticle

@article{bc97e26d14ca43caa5bce5041de3757d,
title = "A projective plane is an outstanding 2-cover",
abstract = "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.",
author = "Z. F{\"u}redi",
year = "1989",
doi = "10.1016/0012-365X(89)90143-X",
language = "English",
volume = "74",
pages = "321--324",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "3",

}

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.

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

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 -