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arXiv · 2208.12864

Ortho-unit polygons can be guarded with at most $\lfloor \frac{n-4}{8} \rfloor$ guards

J. M. Díaz-Báñez·P. Horn·M. A. Lopez·N. Marín·A. Ramírez-Vigueras·O. Solé-Pi·A. Stevens·J. Urrutia
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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 $n \geq 12$ vertices can be guarded with at most $\lfloor \frac{n-4}{8} \rfloor$ guards, which is a tight bound.

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J. M. Díaz-Báñez, P. Horn, M. A. Lopez, N. Marín, A. Ramírez-Vigueras, O. Solé-Pi, A. Stevens, J. Urrutia. 2022-08-26. Ortho-unit polygons can be guarded with at most $\lfloor \frac{n-4}{8} \rfloor$ guards. https://doi.org/10.1007/s00373-024-02880-8

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