A Zero-Free Interval for Chromatic Polynomials of Graphs

1993/09/01 by Bill Jackson · 4 citations
Mathematics · Computer Science · #Graph theory and applications #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Chromatic polynomial #Chromatic scale #Mathematics #Combinatorics #Zero (linguistics) #Graph #Interval (graph theory) #Discrete mathematics

paper · doi:10.1017/s0963548300000705

openalex publication_date 1993/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/16

Abstract

Let G be a graph and P ( G, t ) be the chromatic polynomial of G . It is known that P ( G, t ) has no zeros in the intervals (−∞, 0) and (0, 1). We shall show that P ( G, t ) has no zeros in (1, 32/27]. In addition, we shall construct graphs whose chromatic polynomials have zeros arbitrarily close to 32/27.

Cited by

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• Graph Polynomials and Their Applications I: The Tutte Polynomial
• Chromatic Roots are Dense in the Whole Complex Plane
• Chromatic polynomial [wikipedia]