  We solve the following problem: Can an undirected weighted graph G be parti-
tioned into two non-empty induced subgraphs satisfying minimum constraints for
the sum of edge weights at vertices of each subgraph? We show that this is
possible for all constraints a(x), b(x) satisfying d_G(x) >= a(x) + b(x) +
2W_G(x), for every vertex x, where d_G(x), W_G(x) are, respectively, the sum
and maximum of incident edge weights.
