most recent 30 from http://mathoverflow.net 2013-06-19T09:27:38Z http://mathoverflow.net/feeds/user/18346 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109401/about-a-graph-embedding-from-r3-to/109435#109435 Greg Price 2012-10-12T06:31:24Z 2012-10-12T06:31:24Z

<p>No. Say $L$ consists of $n$ lines, all concurrent but no three coplanar. Then $G$ is the complete graph on $L$, isomorphic to $K_n$. But for $n>3$, $K_n$ has no thrackle. For example, <a href="http://www.ams.org/mathscinet-getitem?mr=1476318" rel="nofollow">Lovász, Pach, and Szegedy</a> showed that a thrackle on $n$ vertices has at most $2n-3$ edges.</p>