Finite ε-unit distance graphs
Finite ε-unit distance graphs
In 2005, Exoo posed the following question. Fix $\epsilon$ with $0\leq\epsilon<1$. Let $G_\epsilon$ be the graph whose vertex set is the Euclidean plane, where two vertices are adjacent iff the Euclidean distance between them lies in the closed interval $[1-\epsilon,1+\epsilon]$. What is the chromatic number $\chi(G_\epsilon)$ of this graph? The …