Upper Bounds on Chromatic Number of $\mathbb{E}^n$ in Low Dimensions
Upper Bounds on Chromatic Number of $\mathbb{E}^n$ in Low Dimensions
Let $\chi(\mathbb{E}^n)$ denote the chromatic number of the Euclidean space $\mathbb{E}^n$, i.e., the smallest number of colors that can be used to color $\mathbb{E}^n$ so that no two points unit distance apart are of the same color. We present explicit constructions of colorings of $\mathbb{E}^n$ based on sublattice coloring schemes …