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Density of Real Zeros of the Tutte Polynomial

Part of: Graph theory

Published online by Cambridge University Press:  09 March 2018

SEONGMIN OK  and
THOMAS J. PERRETT
SEONGMIN OK
Affiliation:
School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea (e-mail: seongmin.ok@gmail.com)
THOMAS J. PERRETT
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kongens Lyngby, Denmark (e-mail: tper@dtu.dk)
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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.

MSC classification

Primary: 05C31: Graph polynomials
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 3 , May 2018 , pp. 398 - 410
Copyright
Copyright © Cambridge University Press 2018 

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