Kauffman's polynomial and alternating links (Q1117502)

In an earlier paper the author showed how the Jones polynomial of a link could be obtained using the Tutte polynomial of a graph G associated with a plane projection of the link. In this paper the author establishes a connection between certain terms of the Kauffman polynomial \(F_ L(a,z)\) of a non-split alternating link L and certain terms of the Tutte polynomial. An important consequence is Theorem 1: The writhe of a reduced alternating diagram of an alternating link L is an isotopy invariant of L. It follows, amongst other things, that the writhe of an amphicheiral alternating knot is zero.