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This is probably a really stupid question, but suppose I have two sets of points in the plane $X$ and $Y$ each with cardinality $|X| = |Y| = n$. For any bipartite matching $M$ between $X$ and $Y$, ...

There are some points in the plane and some of them are connected with segments between them. We look at this structure as a graph immersed into the plane where the points are the vertices and the ...