On the upper chromatic number and multiple blocking sets of PG(n,q)

Zoltán L. Blázsik, Tamás Héger, Tamás Szőnyi

Research output: Contribution to journalArticle

Abstract

We investigate the upper chromatic number of the hypergraph formed by the points and the k-dimensional subspaces of PG(n, q); that is, the most number of colors that can be used to color the points so that every k-subspace contains at least two points of the same color. Clearly, if one colors the points of a double blocking set with the same color, the rest of the points may get mutually distinct colors. This gives a trivial lower bound, and we prove that it is sharp in many cases. Due to this relation with double blocking sets, we also prove that for t ≤ 3/8p + 1, a small t-fold (weighted) (n − k)-blocking set of PG(n, p), p prime, must contain the weighted sum of t not necessarily distinct (n − k)-spaces.

Original languageEnglish
Pages (from-to)118-140
Number of pages23
JournalJournal of Combinatorial Designs
Volume28
Issue number2
DOIs
Publication statusPublished - Feb 1 2020

Keywords

  • multiple weigthed blocking sets
  • projective spaces
  • upper chromatic number

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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