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arXiv · 2202.02919

On some non-rigid unit distance patterns

Nora Frankl·Dora Woodruff
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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 $1/\sqrt{2}$. We also consider a similar problem about $3$-regular unit distance graphs in $\mathbb{R}^3$.

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Nora Frankl, Dora Woodruff. 2023-01-19. On some non-rigid unit distance patterns. https://arxiv.org/abs/2202.02919

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