| Title: | Connected matchings |
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| Authors: | ID Aichholzer, Oswin (Author)
ID Cabello, Sergio (Author)
ID Mészáros, Viola (Author)
ID Schnider, Patrick (Author)
ID Soukup, Jan (Author) |
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| Files: |  PDF - Presentation file, download (995,59 KB)
MD5: 769A17A533415A9DF7B469325D3A7299
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0925772125000124
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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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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| Keywords: | point sets, matchings for point sets, intersection graph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.12.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 15 str. |
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| Numbering: | Vol. 129, article no. 102174 |
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| PID: | 20.500.12556/DiRROS-23895  |
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| UDC: | 519.17:004 |
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| ISSN on article: | 0925-7721 |
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| DOI: | 10.1016/j.comgeo.2025.102174 |
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| COBISS.SI-ID: | 228691203 |
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| Note: |
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| Publication date in DiRROS: | 20.10.2025 |
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| Views: | 199 |
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| Downloads: | 111 |
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| Metadata: |    |
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