Mutual-visibility number conjecture for Cartesian products of paths and cycles

From papers

Let PsP_s be the path on ss vertices and CtC_t the cycle on tt vertices, and let cmu(G)cmu(G) denote the mutual-visibility number of a graph GG. Mutual-visibility number conjecture. If tcge12t cge 12, then

cmu(PscBoxCt)=cmin{3s,2t}.cmu(P_s cBox C_t) = cmin\{3s, 2t\}.

The equality is known in the range 12cletcle1712 cle t cle 17 from the constructions and computational results discussed in the paper, while the assertion for all tcge12t cge 12 remains open.

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Sources & referencesView supporting material

Primary source

Danilo Korže and Aleksander Vesel, “Mutual-visibility sets in Cartesian products of paths and cycles”, arXiv:2309.15201 (2023).

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