Balanced lines in two-coloured point sets
| dc.creator | Orden, David | |
| dc.creator | Ramos, Pedro | |
| dc.creator | Salazar, Gelasio | |
| dc.date | 2009-05-20 | |
| dc.date | 2009-05-22 | |
| dc.date.accessioned | 2026-07-07T13:17:05Z | |
| dc.date.available | 2026-07-07T13:17:05Z | |
| dc.description | Let $B$ and $R$ be point sets (of {\em blue} and {\em red} points, respectively) in the plane, such that $P:=B\cup R$ is in general position, and $|P|$ is even. A line $\ell$ is {\em balanced} if it spans one blue and one red point, and on each open halfplane of $\ell$, the number of blue points minus the number of red points is the same. We prove that $P$ has at least $\min \{|B|,|R|\} $ balanced lines. This refines a result by Pach and Pinchasi, who proved this for the case $|B|=|R|$. | |
| dc.identifier | https://arxiv.org/abs/0905.3380 | |
| dc.identifier | http://arxiv.org/abs/0905.3380 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230999 | |
| dc.subject | Combinatorics | |
| dc.subject | 52A37; 52C30 | |
| dc.title | Balanced lines in two-coloured point sets | |
| dc.type | text |