The Complexity of Computing the Sign of the Tutte Polynomial (and Consequent #P-hardness of Approximation)

On the tutte polynomial of benzenoid chains

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

The Complexity of Computing the Sign of the Tutte

We study the complexity of computing the sign of the Tutte polynomial of a graph. As there are only three possible outcomes (positive, negative, and zero), this seems at first sight more like a decision problem than a counting problem. Surprisingly, however, there are large regions of the parameter space for which computing the sign of the Tutte polynomial is actually #P-hard. As a trivial cons...

Tutte polynomials of wheels via generating functions

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

The complexity of approximating complex-valued Ising and Tutte partition functions with applications to quantum simulation

We study the complexity of approximately evaluating the Ising and Tutte partition functions with complex parameters. Our results are motivated by the study of the quantum complexity classes BQP and IQP. Recent results show how to encode quantum computations as evaluations of partition functions. These results rely on interesting and deep results about quantum computation in order to obtain hard...

Tutte Polynomials of Flower Graphs