The 2-blocking number and the upper chromatic number of PG(2,q)

Gábor Bacsó, Tamás Héger, Tamás Szőnyi

Research output: Article

7 Citations (Scopus)

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 τ2(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 τ2(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 - τ2(Π) + 1 (*) for every plane Π on v points. Let q = ph, p prime. We prove that for Π = PG(2, q), equality holds in (*) if q and p are large enough.

Original languageEnglish
Pages (from-to)585-602
Number of pages18
JournalJournal of Combinatorial Designs
Volume21
Issue number12
DOIs
Publication statusPublished - 2013

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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