论文标题
在某些非刚性单位距离模式上
On some non-rigid unit distance patterns
论文作者
论文摘要
Palsson，Senger和Sheffer提出的最近对ERD的单位距离问题的概括，要求在飞机中具有给定数量的顶点，并以$ 3 $ -SPACE为特定数量的单位距离路径数量。在研究这个问题的一个变体时，我们证明了半径$ 1/\ sqrt {2} $的单位距离路径和周期的数量。我们还考虑了一个类似的问题，大约是$ \ mathbb {r}^3 $中的3美元的单位距离图。
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 $\mathbb{R}^3$.
