Boundary effects in the traveling salesperson problem

Consider a subset F of [0, 1]^2 that is generated by a Poisson point process of constant intensity @l. Denote by @q(@l) the expected length of the shortest tour through F. We prove that for @l large enough, we have [email protected]/@l + 1/K =< [email protected]/@l + K, where c, K are universal constants. This settles a conjecture of Karp.