A zero-free interval for chromatic polynomials
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Abstract It is proved that, for a wide class of near-triangulations of the plane, the chromatic polynomial has no zeros between 2 and 2.5. Together with a previously known result, this shows that the zero of the chromatic polynomial of the octahedron at 2.546602 ··· is the smallest non-integer real zero of any chromatic polynomial of a plane triangulation.
[1] Douglas R. Woodall. An inequality for chromatic polynomials , 1992, Discret. Math..