Abstract
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.
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Giménez, O., Hliněný, P., Noy, M. (2005). Computing the Tutte Polynomial on Graphs of Bounded Clique-Width. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_6
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DOI: https://doi.org/10.1007/11604686_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31000-6
Online ISBN: 978-3-540-31468-4
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