The Complexity of Computing the Sign of the Tutte Polynomial

@article{Goldberg2014TheCO,
title={The Complexity of Computing the Sign of the Tutte Polynomial},
author={Leslie Ann Goldberg and Mark Jerrum},
journal={SIAM J. Comput.},
year={2014},
volume={43},
pages={1921-1952}
}

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 consequence, approximating the polynomial is also #P-hard in this case. Thus, approximately evaluating the… CONTINUE READING