Ortho-Unit Polygons can be Guarded with at most n - 4 8 Guards
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373_2024_2880_ReferencePDF.pdf
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4.51 MB
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Author(s)
Díaz-Báñez, J. M.
Horn, P.
Lopez, M. A.
Marín, N.
Ramírez-Vigueras, A.
Solé-Pi, O.
Stevens, A.
Urrutia, J.
Date Issued
December 29, 2024
Journal
Graphs and Combinatorics
Publisher
Springer Japan
Citation
Díaz-Báñez, J.M., Horn, P., Lopez, M.A. et al. Ortho-Unit Polygons can be Guarded with at most n - 4 8 Guards. Graphs and Combinatorics 41, 15 (2025).
Version
Author's final manuscript
Abstract
Abstract An orthogonal polygon is called an ortho-unit polygon if its vertices have integer coordinates, and all of its edges have length one. In this paper we prove that any ortho-unit polygon with n ≥ 12 vertices can be guarded with at most ⌊ n - 4 8 ⌋ guards, which is a tight bound.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00373-024-02880-8
