# Finding subgraph problem

Is the following a familiar problem ? Given a graph $G = (V, E)$ and a capacity function $c:V \to \mathbb{N}$ find a spanning subgraph $H$ of $G$ such that $1 \leq deg_H(v) \leq c(v)$ for every vertex $v \in V$.

I would like to know if this is an NP-hard problem so any pointer to a similar problem (NP-hard or not) will be very appreciated as well.

Thank you,

• Indeed, by spanning I mean the same set of vertices. $H$ does not have to be connected but its minimum degree must be at least one. The slides seems to be very helpful but ,as far as I can tell, none of the problems that were considered in the slides is exactly the same (or a special case) as I described. – Gilad Dec 9 '17 at 12:41