The Chromatic Number of $K^2(9,4)$ is $11$

Abstract

In 2004, Kim and Nakprasit showed that the chromatic number of $K_2(9,4)$ is at least 11. In this note we present an 11-coloring for $K^2(9,4)$ (the square of the Kneser graph $K(9,4)$). This proves that the chromatic number of $K^2(9,4)$ is $11$.