Abstract
We consider an Erdös type question on k-holes (empty k-gons) in bichromatic point
sets. For a bichromatic point set S = R ∪ B, a balanced 2k-hole in S is spanned by
k points of R and k points of B. We show that if R and B are linearly separable
and |R| = |B| = n, then the number of balanced 6-holes in S is at least 1
15 n2 −Θ(n).
sets. For a bichromatic point set S = R ∪ B, a balanced 2k-hole in S is spanned by
k points of R and k points of B. We show that if R and B are linearly separable
and |R| = |B| = n, then the number of balanced 6-holes in S is at least 1
15 n2 −Θ(n).
| Original language | English |
|---|---|
| Pages (from-to) | 181-186 |
| Journal | Electronic Notes in Discrete Mathematics |
| Volume | 44 |
| DOIs | |
| Publication status | Published - 2013 |
Fields of Expertise
- Information, Communication & Computing