Report
On the upper chromatic number and multiplte blocking sets of PG($n,q$)
| العنوان: | On the upper chromatic number and multiplte blocking sets of PG($n,q$) |
|---|---|
| المؤلفون: | Blázsik, Zoltán L., Héger, Tamás, Szőnyi, Tamás |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | We investigate the upper chromatic number of the hypergraph formed by the points and the $k$-dimensional subspaces of $\mathrm{PG}(n,q)$; 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 $t\leq \frac38p+1$, a small $t$-fold (weighted) $(n-k)$-blocking set of $\mathrm{PG}(n,p)$, $p$ prime, must contain the weighted sum of $t$ not necessarily distinct $(n-k)$-spaces. Comment: 21 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1909.02867 |
| رقم الانضمام: | edsarx.1909.02867 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |