2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64059Let $L_N = L_{MBM}(X_1,..., X_N; Y_1,..., Y_N)$ be the minimum length of a bipartite matching between two sets of points in $\mathbf{R}^d$, where $X_1,..., X_N,...$ and $Y_1,..., Y_N,...$ are random points independently and uniformly distributed in $[0,1]^d$. We prove that for $d \ge 3$, $L_N/N^{1-1/d}$ converges with probability one to a constant $β_{MBM}(d)>0$ as $N\to \infty $.To appear in CombinatoricaCombinatoricsOptimization and ControlProbabilityF.2.2, G.3text