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T. Let, be the set of all different rooted spanning trees of G. We deduce in Corollary 13 an exact algorithm for the (k, D)-family-matching problem for G

. Corollary, that is an optimal solution for the (k, D)-family-matching problem for G, if

T. I. For-every-i-?-{1, k}. By construction of T , S is an admissible solution for the D-family-matching problem for G constrained by