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A well-known theorem of Nash-Williams and Tutte gives a necessary and sufficient condition for the existence of k edge-disjoint spanning trees in an undirected graph. A corollary of this theorem is that every 2k-edge-connected graph has k edge-disjoint spanning trees. The authors show that the splitting-off theorem of Mader in undirected graphs implies a generalization of this to finding k edge-disjoint Steiner forests in Eulerian graphs. This leads to new 2-approximation rounding algorithms for constrained 0-1 forest problems considered by Goemans and Williamson. These algorithms also produce approximate integer decompositions of fractional solutions.
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