Connected matchings

Aichholzer, Oswin (author), Cabello, Sergio (author), Mészáros, Viola (author), Schnider, Patrick (author), Soukup, Jan (author)

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.

• Language: English
• Keywords: point sets, matchings for point sets, intersection graph
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 15 str.
• Numbering: Vol. 129, art. 102174
• PID: 20.500.12556/RUL-167823
• UDC: 519.17:004
• ISSN on article: 0925-7721
• DOI: 10.1016/j.comgeo.2025.102174
• COBISS.SI-ID: 228691203
• Publication date in RUL: 13.03.2025

Record is a part of a journal

• Title: Computational geometry
• Shortened title: Comput. geom.
• Publisher: Elsevier
• ISSN: 0925-7721
• COBISS.SI-ID: 14903301

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.