The guard conjecture for integral orthogonal polygons
Let be an integral orthogonal polygon, meaning that all its edges have integer length, and let be its perimeter. The guard conjecture. The polygon can always be guarded with at most
guards. The best bound established in the paper is , while the conjectured bound is motivated by integral versions of orthogonal comb polygons requiring guards and remains open.
References
Primary source
J. M. Díaz-Báñez, P. Horn, M. A. Lopez, N. Marín, A. Ramírez-Vigueras, O. Solé-Pi, A. Stevens and J. Urrutia, “Ortho-unit polygons can be guarded with at most n-48 guards”, arXiv:2208.12864 (2025).
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