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arXiv · 2410.06139

Flips in Odd Matchings

Oswin Aichholzer·Anna Brötzner·Daniel Perz·Patrick Schnider
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Abstract

Let $\mathcal{P}$ be a set of $n=2m+1$ points in the plane in general position. We define the graph $GM_\mathcal{P}$ whose vertex set is the set of all plane matchings on $\mathcal{P}$ with exactly $m$ edges. Two vertices in $GM_\mathcal{P}$ are connected if the two corresponding matchings have $m-1$ edges in common. In this work we show that $GM_\mathcal{P}$ is connected and give an upper bound of $O(n^2)$ on its diameter. Moreover, we present a tight bound of $\Theta(n)$ for the diameter of the flip graph of points in convex position.

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Oswin Aichholzer, Anna Brötzner, Daniel Perz, Patrick Schnider. 2024-10-08. Flips in Odd Matchings. https://arxiv.org/abs/2410.06139

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