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 \(F(G,t)\in \{(t-1)^{2},(t-1)(t-2\}\) if \(m=n+1\). It is shown that if \(m\geq n+2\), 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 \(0\leq i\leq m-n+1\).
scientific article; zbMATH DE number 5143580