Year: 2024
Type: preprint
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 $Θ(n)$ for the diameter of the flip graph of points in convex position.
Source: arXiv (Cornell University)
Institutions: Graz University of Technology, University of Perugia, ETH Zurich
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Austrian Science Fund, Vetenskapsrådet
OpenAlex ID: W4403344638