most citedCoverings of planar and three-dimensional sets with subsets of smaller diameter

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math.MG2024

Optimal partitions of the flat torus into parts of smaller diameter

Dmitry Protasov, Alexander Tolmachev, Vsevolod Voronov

We consider the problem of partitioning a two-dimensional flat torus into sets in order to minimize the maximal diameter of a part. For we give numerical…

math.MG2022★ 6 cited

Coverings of planar and three-dimensional sets with subsets of smaller diameter

Alexander Tolmachev, Dmitry Protasov, Vsevolod Voronov

Quantitative estimates related to the classical Borsuk problem of splitting set in Euclidean space into subsets of smaller diameter are considered. For a given there is a minim…