Flips in Odd Matchings

O. Aichholzer, A. Brötzner, D. Perz, and P. Schnider

Abstract:

Let $P$ be a set of $n=2m+1$ points in the plane in general position. We define the graph $GM_P$ whose vertex set is the set of all plane matchings on $P$ with exactly $m$ edges. Two vertices in $GM_P$ are connected if the two corresponding matchings have $m-1$ edges in common. In this work we show that $GM_P$ is connected.

Reference: O. Aichholzer, A. Brötzner, D. Perz, and P. Schnider. Flips in odd matchings. In Proceedings of the 40th European Workshop on Computational Geometry (EuroCG 2024), pages 59:1-59:6, 2024.