English

Ball packings with high chromatic numbers from strongly regular graphs

Combinatorics 2018-08-20 v5 Metric Geometry

Abstract

Inspired by Bondarenko's counter-example to Borsuk's conjecture, we notice some strongly regular graphs that provide examples of ball packings whose chromatic numbers are significantly higher than the dimensions. In particular, from generalized quadrangles we obtain unit ball packings in dimension q3q2+qq^3-q^2+q with chromatic number q3+1q^3+1, where qq is a prime power. This improves the previous lower bound for the chromatic number of ball packings.

Keywords

Cite

@article{arxiv.1502.02070,
  title  = {Ball packings with high chromatic numbers from strongly regular graphs},
  author = {Hao Chen},
  journal= {arXiv preprint arXiv:1502.02070},
  year   = {2018}
}

Comments

4 pp. Section 4 removed due to mistake

R2 v1 2026-06-22T08:24:21.555Z