Decomposing Weighted Graphs
Abstract
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 dG(x) >= a(x) + b(x) + 2WG(x), for every vertex x, where dG(x), WG(x) are, respectively, the sum and maximum of incident edge weights.
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