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April 2019 On a Conjecture of Sokal Concerning Roots of the Independence Polynomial
Han Peters, Guus Regts
Michigan Math. J. 68(1): 33-55 (April 2019). DOI: 10.1307/mmj/1541667626

Abstract

A conjecture of Sokal [24], regarding the domain of nonvanishing for independence polynomials of graphs, states that given any natural number Δ3, there exists a neighborhood in C of the interval [0,(Δ1)Δ1/(Δ2)Δ) on which the independence polynomial of any graph with maximum degree at most Δ does not vanish. We show here that Sokal’s conjecture holds, as well as a multivariate version, and prove the optimality for the domain of nonvanishing. An important step is to translate the setting to the language of complex dynamical systems.

Citation

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Han Peters. Guus Regts. "On a Conjecture of Sokal Concerning Roots of the Independence Polynomial." Michigan Math. J. 68 (1) 33 - 55, April 2019. https://doi.org/10.1307/mmj/1541667626

Information

Received: 30 January 2017; Revised: 21 June 2018; Published: April 2019
First available in Project Euclid: 8 November 2018

zbMATH: 07155457
MathSciNet: MR3934603
Digital Object Identifier: 10.1307/mmj/1541667626

Subjects:
Primary: 05C31, 37F10
Secondary: 82B20

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 1 • April 2019
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