The Beraha number B10B_{10} is a chromatic root

preprint2016arXivOpen access

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.

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