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Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width

Published online by Cambridge University Press:  01 September 1998

Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB, England (e-mail:


It is known that evaluating the Tutte polynomial, T(G; x, y), of a graph, G, is #P-hard at all but eight specific points and one specific curve of the (x, y)-plane. In contrast we show that if k is a fixed constant then for graphs of tree-width at most k there is an algorithm that will evaluate the polynomial at any point using only a linear number of multiplications and additions.

Research Article
1998 Cambridge University Press

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