Abstract
AbstractA 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 $$1/{\sqrt{2}}$$
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2
. We also consider a similar problem about 3-regular unit distance graphs in $$\mathbb {R}^3$$
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3
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Funder
National Science Foundation
European Research Council
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science
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