Density of Real Zeros of the Tutte Polynomial

Seongmin Ok, Thomas Perrett*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.

Original languageEnglish
JournalCombinatorics, Probability & Computing
Volume27
Issue number3
Pages (from-to)398-410
ISSN0963-5483
DOIs
Publication statusPublished - 2018

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