Series-parallel posets and the Tutte polynomial Original Research Article

We investigate the Tutte polynomial f(P; t, z) of a series-parallel partially ordered set P. We show that f(P) can be computed in polynomial-time when P is series-parallel and that series-parallel posets having isomorphic deletions and contractions are themselves isomorphic. A formula for f(P∗) in terms of f(P) is obtained and shows these two polynomials factor over Z[t, z] the same way. We examine several subclasses of the class of series-parallel posets, proving that f(P) ≠ f(Q) for non-isomorphic posets P and Q in the largest of these classes. We also give excluded subposet characterizations of the various subclasses.