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 ) ∈ { ( 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 .