New lower bounds on $\chi(R^d)$ for $d=8 \dots 12$

TL;DR

This paper improves the known lower bounds for the chromatic number of Euclidean space in dimensions 8 to 12 through extensive computational methods.

Contribution

It provides new, tighter lower bounds for the chromatic number in specific small dimensions, advancing understanding in geometric graph theory.

Findings

Improved lower bounds for dimensions 8 to 12

Extensive computational approach using Sage

Enhanced understanding of Euclidean space coloring

Abstract

We improve the best lower bounds on the chromatic number of Euclidean space in small dimensions. The new results depend on extensive computations in Sage.