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Frankl, Nóra and Woodruff, Dora
(2023).
DOI: https://doi.org/10.1007/s00454-023-00503-2
Abstract
A recent generalization of the Erdős Unit Distance Problem, proposed by Palsson, Senger, and Sheffer, asks for the maximum number of unit distance paths with a given number of vertices in the plane and in 3-space. Studying a variant of this question, we prove sharp bounds on the number of unit distance paths and cycles on the sphere of radius 1/√2. We also consider a similar problem about 3-regular unit distance graphs in R3.