Bounds for the coefficients of flow polynomials

Let G be any connected bridgeless (n, m)-graph which may have loops and multiedges. It is known that the flow polynomial F(G, t) of G is a polynomial of degree m - n + 1; F(G, t) = t - 1 if m = n; and F(G, t) is an element of {(t - 1)(2), (t - 1)(t - 2)} if m = n + 1. This paper shows that if m >= n + 2, then the absolute value of the coefficient of t(i) in the expansion of F(G, t) is bounded above by the coefficient of t(i) in the expansion of (t + 1)(t + 2)(t + 3)(t + 4)(m-n-2) for each i with 0 <= i <= m - n + 1. (c) 2006 Elsevier Inc. All rights reserved.