# Improved lower bounds for the chromatic number of several small dimensional Euclidean spaces

## April 14, 2015

The chromatic number of the $n$-dimensional Euclidean space, denoted $\chi(\mathbb{R}^n)$, is the minimum number of colors that can be assigned to the points of $\mathbb{R}^n$ so that no two points at distance one receive the same color. In this talk we present better lower bounds for $\chi(\mathbb{R}^n)$ for several small values of $n$.

Joint work with Geoffrey Exoo, Indiana State University.