Timeline for Minimal number of edges for complete linear hypergraphs
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2016 at 0:25 | comment | added | Pat Devlin | This same argument can be pushed to show a lower bound of about $\sqrt{2n}$. | |
| Nov 21, 2016 at 23:07 | comment | added | Aaron Meyerowitz | This is a grid of $2k$ lines on $k^2$ points plus a 2 point line "$h,v$" with $h$ a point common to all horizontal lines and $v$ common to all vertical lines. | |
| Nov 21, 2016 at 21:58 | comment | added | domotorp | Actually, I was just thinking of a grid... | |
| Nov 21, 2016 at 19:37 | comment | added | Aaron Meyerowitz | Here is an example with $n=k^2+2$ and $2k+1$ lines. Start with two points on the $x$ axis. Draw $k$ lines of positive slope leaving one and $k$ of negative slope leaving the other. Keep only the intersection points. | |
| Nov 21, 2016 at 16:58 | comment | added | Dominic van der Zypen | Thanks -- what I don't see yet is how to cover $n^2$ points, say, with $2n$ edges such that every pair of edges intersect and such that every point is covered by at least $2$ edges. Can you give a short example on that? | |
| Nov 21, 2016 at 14:30 | history | answered | domotorp | CC BY-SA 3.0 |