ScholarLens Back to search
2007•Combinatorics Probability ComputingRequires access

Regions Without Complex Zeros for Chromatic Polynomials on Graphs with Bounded Degree

Roberto Fernández, Aldo Procacci

Open publisher page 36 citations

Abstract

We prove that the chromatic polynomial $P_\mathbb{G}(q)$ of a finite graph $\mathbb{G}$ of maximal degree Δ is free of zeros for |q| ≥C*(Δ) with This improves results by Sokal and Borgs. Furthermore, we present a strengthening of this condition for graphs with no triangle-free vertices.

About this research paper

What this paper is about

We prove that the chromatic polynomial $P_\mathbb{G}(q)$ of a finite graph $\mathbb{G}$ of maximal degree Δ is free of zeros for |q| ≥C*(Δ) with This improves results by Sokal and Borgs. Furthermore, we present a strengthening of this condition for graphs with no triangle-free vertices.

Why it matters

OpenAlex reports 36 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We prove that the chromatic polynomial $P_\mathbb{G}(q)$ of a finite graph $\mathbb{G}$ of maximal degree Δ is free of zeros for |q| ≥C*(Δ) with This improves results by Sokal and Borgs. Furthermore, we present a strengthening of this condition for graphs with no triangle-free vertices.

Key concepts: Chromatic polynomial, Chromatic scale, Mathematics, Degree (music), Combinatorics, Bounded function, Graph, Discrete mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Regions Without Complex Zeros for Chromatic Polynomials on Graphs with Bounded Degree — Research Paper | ScholarLens