# Degree constrained edge partitioning (version 2)

Given a graph $G=(V,E)$ with real-valued (positive or negative) weights assigned to its edges, we want to remove a set of edges so that the sum of the remaining edges is minimized and the degree of any vertex should be different than 1 (i.e. 0 or more than 1) in the final graph.

I'm interested in the complexity of this problem.

Note that this problem is a slight variation of this.

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So there should be no leaf vertices in the final graph. Isolated vertices are OK. –  eakbas Apr 9 '10 at 1:10
Didn't you show in you answer to the linked question that "minimum subgraph of degree $\ge 2$" is polynomial? –  Sergei Ivanov Apr 9 '10 at 8:41