The Beraha number B₁₀ is a chromatic root

2016/11/07 by Gordon Royle, Royle, Gordon
Engineering · Mathematics · #05C15 #05C31 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1611.01941

openalex publication_date 2016/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note exhibits graphs whose chromatic polynomials have the Beraha number B₁₀ = (5 + √(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.

Related

• Chromatic roots at 2 and at the Beraha number B₁₀
• Extension to the Beraha-Kahane-Weiss Theorem with Applications
• Some applications of the chromatic polynomials
• Polynomial bounds for chromatic number. V. Excluding a tree of radius two and a complete multipartite graph
• The b-Chromatic Number of Certain Graphs and Digraphs