On Some Non-Rigid Unit Distance Patterns

Frankl, Nóra and Woodruff, Dora (2023). On Some Non-Rigid Unit Distance Patterns. Discrete & Computational Geometry (Early access).

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.

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