Hard enumeration problems in geometry and combinatorics
SIAM Journal on Algebraic and Discrete Methods
A Tutte polynomial for signed graphs
Discrete Applied Mathematics - Combinatorics and complexity
Complexity and real computation
Complexity and real computation
A Tutte Polynomial for Coloured Graphs
Combinatorics, Probability and Computing
Inapproximability of the Tutte polynomial
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials
Theory of Computing Systems
Complexity of the cover polynomial
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
An extension of the bivariate chromatic polynomial
European Journal of Combinatorics
A Most General Edge Elimination Polynomial - Thickening of Edges
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
The enumeration of vertex induced subgraphs with respect to the number of components
European Journal of Combinatorics
The complexity of the cover polynomials for planar graphs of bounded degree
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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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.