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{\bf Alex Brodsky, Stephane Durocher and Ellen Gethner}
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{\bf The Rectilinear Crossing Number of $K_{10}$ is $62$}
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The rectilinear crossing number of a graph $G$ is the minimum number of
edge crossings that can occur in any drawing of $G$ in which the edges
are straight line segments and no three vertices are collinear. This
number has been known for $G=K_n$ if $n \leq 9$.  Using a combinatorial
argument we show that for $n=10$ the number is 62.  

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