The graph of triangulations of a convex polygon
Proceedings of the twelfth annual symposium on Computational geometry
Sequences of spanning trees and a fixed tree theorem
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
On the number of crossing-free matchings, (cycles, and partitions)
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Encompassing colored planar straight line graphs
Computational Geometry: Theory and Applications
Augmenting the connectivity of geometric graphs
Computational Geometry: Theory and Applications
Compatible geometric matchings
Computational Geometry: Theory and Applications
Transforming spanning trees: A lower bound
Computational Geometry: Theory and Applications
Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry
Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry
Pointed binary encompassing trees: Simple and optimal
Computational Geometry: Theory and Applications
Transforming spanning trees and pseudo-triangulations
Information Processing Letters
Disjoint compatible geometric matchings
Proceedings of the twenty-seventh annual symposium on Computational geometry
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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 = M1, ..., Mk = M' such that Mi-1 is compatible with Mi. This implies the connectivity of the compatible bichromatic matching graph containing one node for each BR-matching and an edge joining each pair of compatible BR-matchings, thereby answering the open problem posed by Aichholzer et al. in their paper "Compatible matchings for bichromatic plane straight-line graphs".