Ball packings with high chromatic numbers from strongly regular graphs

Hao Chen

Published 2015-02-06Version 1

Inspired by Bodarenko's counter-example to Borsuk's conjecture, we notice some strongly regular graphs that provide examples of ball packings whose chromatic numbers is significantly higher than the dimension. In particular, we obtain from generalized quadrangles the first non-constant lower bound for the difference between the chromatic number and the dimension.