  One way to speed up the calculation of optimal TSP tours in practice is
eliminating edges that are certainly not in the optimal tour as a preprocessing
step. In order to do so several edge elimination approaches have been proposed
in the past. In this work we investigate two of them in the scenario where the
input consists of $n$ independently distributed random points in the
2-dimensional unit square with bounded density function from above and below by
arbitrary positive constants. We show that after the edge elimination procedure
of Hougardy and Schroeder the expected number of remaining edges is
$\Theta(n)$, while after that the non-recursive part of Jonker and Volgenant
the expected number of remaining edges is $\Theta(n^2)$.
