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Dec 11, 2013 at 13:23 comment added David E Speyer Which was incredibly useful in clearing up my misconceptions. If another answer comes along to do the $k$-cycle case, I will certainly give it an additional bounty.
Dec 11, 2013 at 13:22 comment added Dag Oskar Madsen @David Speyer It's too generous of you to give me the bounty. I only helped with a special case of your general question.
Dec 11, 2013 at 12:39 history bounty ended David E Speyer
Dec 11, 2013 at 12:39 vote accept David E Speyer
Dec 10, 2013 at 16:32 history edited Dag Oskar Madsen CC BY-SA 3.0
are -> is
Dec 10, 2013 at 16:22 comment added David E Speyer Thanks! I don't know about $K_{6,6}$, but $K_{7,7}$ is easy: Take the Fano plane and the dual Fano plane. For a point $p$ and a line $\ell$, put $p \to \ell$ if $p$ is on $\ell$ and $\ell \to p$ otherwise. Any two points are on a common line, and any two lines both miss some common point. I'm waiting a little bit on the bounty to see if anything more awesome turns up.
Dec 10, 2013 at 16:21 history edited Dag Oskar Madsen CC BY-SA 3.0
orientation of edges
Dec 10, 2013 at 15:55 history undeleted Dag Oskar Madsen
Dec 10, 2013 at 15:55 history edited Dag Oskar Madsen CC BY-SA 3.0
added 54 characters in body
Dec 10, 2013 at 15:45 history deleted Dag Oskar Madsen via Vote
Dec 10, 2013 at 15:41 history answered Dag Oskar Madsen CC BY-SA 3.0