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August 2021 Cayley Trees do Not Determine the Maximal Zero-Free Locus of the Independence Polynomial
Pjotr Buys
Michigan Math. J. 70(3): 635-648 (August 2021). DOI: 10.1307/mmj/1599206419

Abstract

In [PR19], Peters and Regts confirmed a conjecture by Sokal [Sok01] by showing that for every ΔZ3, there exists a complex neighborhood of the interval [0,(Δ1)Δ1/(Δ2)Δ) on which the independence polynomial is nonzero for all graphs of maximum degree Δ. Furthermore, they gave an explicit neighborhood UΔ containing this interval on which the independence polynomial is nonzero for all finite rooted Cayley trees with branching number Δ. The question remained whether UΔ would be zero-free for the independence polynomial of all graphs of maximum degree Δ. In this paper, we show that this is not the case.

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Pjotr Buys. "Cayley Trees do Not Determine the Maximal Zero-Free Locus of the Independence Polynomial." Michigan Math. J. 70 (3) 635 - 648, August 2021. https://doi.org/10.1307/mmj/1599206419

Information

Received: 1 May 2019; Revised: 17 June 2020; Published: August 2021
First available in Project Euclid: 4 September 2020

Digital Object Identifier: 10.1307/mmj/1599206419

Subjects:
Primary: 05C31
Secondary: 30D05

Rights: Copyright © 2021 The University of Michigan

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Vol.70 • No. 3 • August 2021
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