# On Coloring the Odd-Distance Graph

## TL;DR

This paper proves using spectral methods that the odd-distance graph cannot be colored with finitely many measurable colors, highlighting a fundamental limitation in graph coloring.

## Contribution

The paper introduces a spectral technique-based proof demonstrating the impossibility of finitely measurable coloring for the odd-distance graph.

## Key findings

- No finite measurable coloring exists for the odd-distance graph
- Spectral techniques effectively prove coloring limitations
- Advances understanding of geometric graph coloring constraints

## Abstract

We present a proof, using spectral techniques, that there is no finite measurable coloring of the odd-distance graph.