Abstract
We discuss the complexity of computing various graph polynomials of graphs of fixed clique-width. We show that the chromatic polynomial, the matching polynomial and the two-variable interlace polynomial of a graph G of clique-width at most k with n vertices can be computed in time O(n f( k)), where f(k) ≤3 for the inerlace polynomial, f(k) ≤2k+1 for the matching polynomial and f(k) ≤3 2k + 2 for the chromatic polynomial.
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Makowsky, J.A., Rotics, U., Averbouch, I., Godlin, B. (2006). Computing Graph Polynomials on Graphs of Bounded Clique-Width. In: Fomin, F.V. (eds) Graph-Theoretic Concepts in Computer Science. WG 2006. Lecture Notes in Computer Science, vol 4271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11917496_18
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DOI: https://doi.org/10.1007/11917496_18
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