We study minimum weight bipartite matchings of size $n$ in the weighted
bipartite graph $K(n,n+1)$. These matchings played an important role in
a proof of Parisi's conjecture for the Random Assignment Problem. We
show that there is a certain minimality in the number of edges that
participate in these minimum weight matchings. And, for a special case of edge
weights on $K(n,n+1)$, we prove that the minimum matchings asymptotically
convergeto an elegant limit.

Keywords:

Phase Transition;Computation;Reconstruction

Lecture #10872

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