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Density of real zeros of the Tutte polynomial. (English) Zbl 1388.05093
Summary: 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 B. Jackson and A. D. Sokal [J. Comb. Theory, Ser. B 99, No. 6, 869–903 (2009; Zbl 1221.05144)] except for one region which is related to an open problem on flow polynomials.

MSC:
05C31 Graph polynomials
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