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Flips in Odd Matchings (2410.06139v1)
Published 8 Oct 2024 in cs.CG and math.CO
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 $O(n2)$ on its diameter. Moreover, we present a tight bound of $\Theta(n)$ for the diameter of the flip graph of points in convex position.