Connected Matchings
| Autor: | Aichholzer, Oswin, Cabello, Sergio, Mészáros, Viola, Schnider, Patrick, Soukup, Jan |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 20 pages, 14 figures; preliminary version in EuroCG 2024 |
| Databáze: | arXiv |
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