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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