### Abstract

A twofold blocking set (double blocking set) in a finite projective plane Π is a set of points, intersecting every line in at least two points. The minimum number of points in a double blocking set ofΠis denoted by τ_{2}(Π). Let PG(2, q) be the Desarguesian projective plane over GF(q), the finite field of q elements. We show that if q is odd, not a prime, and r is the order of the largest proper subfield of GF(q), then τ_{2}(PG(2, q)) ≤ 2(q + (q - 1)/(r - 1)). For a finite projective plane Π, let χ (Π) denote the maximum number of classes in a partition of the point-set, such that each line has at least two points in some partition class. It can easily be seen that χ(Π) ≥ v - τ_{2}(Π) + 1 (*) for every plane Π on v points. Let q = p^{h}, p prime. We prove that for Π = PG(2, q), equality holds in (*) if q and p are large enough.

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

Pages (from-to) | 585-602 |

Number of pages | 18 |

Journal | Journal of Combinatorial Designs |

Volume | 21 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2013 |

### Keywords

- Double blocking set
- Finite projective plane
- Hypergraph
- Upper chromatic number

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'The 2-blocking number and the upper chromatic number of PG(2,q)'. Together they form a unique fingerprint.

## Cite this

*Journal of Combinatorial Designs*,

*21*(12), 585-602. https://doi.org/10.1002/jcd.21347