Computing the Tutte Polynomial on Graphs of Bounded Clique-Width

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The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded tree-width. The notion of clique-width extends the definition of cograhs (graphs without induced P 4), and it is a more general notion than that of tree-width. We show a subexponential algorithm (running in time expO(n 2/3)) for computing the Tutte polynomial on cographs. The algorithm can be extended to a subexponential algorithm computing the Tutte polynomial on on all graphs of bounded clique-width. In fact, our algorithm computes the more general U-polynomial.

2000 Math Subjects Classification: 05C85, 68R10.