On the algebraic complexity of some families of coloured Tutte polynomials

We investigate the coloured Tutte polynomial in Valiant's algebraic framework of NP-completeness. Generalising the well-known relationship between the Tutte polynomial and the partition function from the Ising model, we establish a reduction from the permanent to the coloured Tutte polynomial, thus showing that its evaluation is a VNP-complete problem.

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