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.

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.