# Orientation-compatible w-vertex cover

Given a digraph D=(V,A) and non-negative even-valued arc weights $w_a\ (a \in A)$, can we find in polynomial time a w-vertex cover $x$ of the underlying undirected graph with the additional property that for every node v with $x_v\gt0$ there is an arc $uv\in A$ with $x_u+x_v=w_a$?