Bounding the coefficients of the characteristic polynomials of simple binary matroids

Abstract

We give an upper bound and a class of lower bounds on the coefficients of the characteristic polynomial of a simple binary matroid. This generalizes the corresponding bounds for graphic matroids of Li and Tian (1978) [3], as well as a matroid lower bound of Bjrner (1980) [1] for simple binary matroids. As the flow polynomial of a graph G is the characteristic polynomial of the dual matroid M*(G), the bound applies to flow polynomials. © 2012 Elsevier B.V. All rights reserved.