  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 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 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.
