English

The Beraha number $B_{10}$ is a chromatic root

Combinatorics 2016-11-08 v1

Abstract

This note exhibits graphs whose chromatic polynomials have the Beraha number B10=(5+5)/2B_{10} = (5 + \sqrt{5})/2 as a root. It was previously known that no other non-integer Beraha number is a chromatic root, and so these examples complete the determination of precisely which Beraha numbers can be chromatic roots.

Cite

@article{arxiv.1611.01941,
  title  = {The Beraha number $B_{10}$ is a chromatic root},
  author = {Gordon Royle},
  journal= {arXiv preprint arXiv:1611.01941},
  year   = {2016}
}
R2 v1 2026-06-22T16:43:51.536Z