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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References
Andrews, G.E.: The theory of partitions. Cambridge U. Press, Cambridge (1984)
Andrzejak, A.: An Algorithm for the Tutte Polynomials of Graphs of Bounded Treewidth. Discrete Math. 190, 39–54 (1998)
Courcelle, B., Makowsky, J.A., Rotics, U.: Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width. Theory Comput. Systems 33, 125–150 (2000)
Courcelle, B., Olariu, S.: Upper bounds to the clique width of graphs. Discrete Appl. Math. 101, 77–114 (2000)
Giménez, O., Noy, M.: On the complexity of computing the Tutte polynomial of bicircular matroids. Combin. Probab. Computing (to appear)
Giménez, O., Hliněný, P., Noy, M.: Computing the Tutte Polynomial on graphs of Bounded Clique-Width (2005) (manuscript)
Hliněný, P.: The Tutte Polynomial for Matroids of Bounded Branch-Width, Combin. Probab. Computing (2005) (to appear)
Jaeger, F., Vertigan, D.L., Welsh, D.J.A.: On the Computational Complexity of the Jones and Tutte Polynomials. Math. Proc. Camb. Phil. Soc. 108, 35–53 (1990)
Kobler, D., Rotics, U.: Edge dominating set and colorings on graphs with fixed clique-width. Discrete Applied Math. 126, 197–221 (2003)
van Lint, J.H., Wilson, R.M.: A Course in Combinatorics. Cambridge University Press, Cambridge (1992)
Noble, S.D.: Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width. Combin. Probab. Computing 7, 307–321 (1998)
Noble, S.D., Welsh, D.J.A.: A weighted graph polynomial from chromatic invariants of knots. Ann. Inst. Fourier (Grenoble) 49, 1057–1087 (1999)
Oum, S.-I., Seymour, P.D.: Approximating Clique-width and Branch-width (2004) (submitted)
Oum, S.-I.: Approximating Rank-width and Clique-width Quickly. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 49–58. Springer, Heidelberg (2005)
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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
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