The N/6N/6 guard conjecture for integral orthogonal polygons

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Let PP be an integral orthogonal polygon, meaning that all its edges have integer length, and let NN be its perimeter. The N/6N/6 guard conjecture. The polygon PP can always be guarded with at most

⌊N6⌋\left\lfloor \frac{N}{6} \right\rfloor

guards. The best bound established in the paper is ⌊N/5⌋\lfloor N/5\rfloor, while the conjectured N/6N/6 bound is motivated by integral versions of orthogonal comb polygons requiring N/6N/6 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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