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.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics