6 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    36th International Symposium on Theoretical Aspects of Computer Science: STACS 2019, March 13-16, 2019, Berlin, Germany

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    Complexity of the Bollobás-Riordan Polynomial -- Exceptional Points and Uniform Reductions

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    The coloured Tutte polynomial by Bollobás and Riordan is, as a generalization of the Tutte polynomial, the most general graph polynomial for coloured graphs that satisfies certain contraction-deletion identities. Jaeger, Vertigan, and Welsh showed that the classical Tutte polynomial is #P-hard to evaluate almost everywhere by establishing reductions along curves and lines. We establish a similar result for the coloured Tutte polynomial on integral domains. To capture the algebraic flavour and the uniformity inherent in this type of result, we introduce a new kind of reductions, uniform algebraic reductions, that are well-suited to investigate the evaluation complexity of graph polynomials. Our main result identifies a small, algebraic set of exceptional points and says that the evaluation problem of the coloured Tutte is equivalent for all non-exceptional points, under polynomial-time uniform algebraic reductions

    Subject Index Volumes 1–200

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