Luis Barba

For a set *R* of *n* red points and a set *B* of *n* blue points, a *BR*-matching is a non-crossing geometric perfect matching where each segment has one endpoint in *B* and one in *R*. Two *BR*-matchings are compatible if their union is also non-crossing. We prove that, for any two distinct *BR*-matchings *M* and *M'*, there exists a sequence of *BR*-matchings *M = M _{1} ,..., M_{k} = M'* such that