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arXiv · 2407.06131

Connected Matchings

Oswin Aichholzer·Sergio Cabello·Viola Mészáros·Patrick Schnider·Jan Soukup
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Abstract

We show that each set of $n\ge 2$ points in the plane in general position has a straight-line matching with at least $(5n+1)/27$ edges whose segments form a connected set, and such a matching can be computed in $O(n \log n)$ time. As an upper bound, we show that for some planar point sets in general position the largest matching whose segments form a connected set has $\lceil \frac{n-1}{3}\rceil$ edges. We also consider a colored version, where each edge of the matching should connect points with different colors.

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Oswin Aichholzer, Sergio Cabello, Viola Mészáros, Patrick Schnider, Jan Soukup. 2025-02-24. Connected Matchings. https://arxiv.org/abs/2407.06131

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