On the upper chromatic number and multiple blocking sets of PG(n,q)
WoS ID: 000495479900001
Scopus ID: 85075040960
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 <= 38p+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.