# Minimum-weight disjoint union of perfect matchings

Is there a counter example or proof for the claim that the lightest edge-disjoint union of a pair of perfect matchings contains the edges of the lightest perfect matching in a finite complete graph with $$2n$$ vertices and positive edge-weights?

• The context here is a weighted graph? Apr 13 at 12:25
• @GerryMyerson yes, sorry if that isn't clear from the question; I will edit the question accordingly. Apr 13 at 12:31