# Balanced weight perfect matching

Given an undirected graph $$G = (V,E)$$, edge weight $$w_e \ \forall e \in E$$, I'm interested in the following problem.

Find a perfect matching $$M \subseteq E$$ that minimizes $$(\max_{e \in M} w_e - \min_{e \in M} w_e)$$.

Does this problem generalize/reduce to an existing problem? I can find max weight perfect matching, but not exactly a "balanced weight perfect matching". Any thoughts would be helpful.