Graph polynomials which are definable in Monadic Second Order Logic (MSOL) on the vocabulary of graphs are Fixed-Parameter Tractable (FPT) with respect to clique-width. In contrast, graph polynomials which are definable in MSOL on the vocabulary of hypergraphs are fixed-parameter tractable with respect to tree-width, but not necessarily with respect to clique-width. No algorithmic meta-theorem is known for the computation of graph polynomials definable in MSOL on the vocabulary of hypergraphs with respect to clique-width. We define an infinite class of such graph polynomials extending the class of graph polynomials definable in MSOL on the vocabulary of graphs and prove that they are Fixed-Parameter Polynomial Time (FPPT or XP) computable, i.e. that they can be computed in time O(nf(k)), where n is the number of vertices and k is the clique-width.
CITATION STYLE
Kotek, T., & Makowsky, J. A. (2016). Efficient computation of generalized ising polynomials on graphs with fixed clique-width. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9541, pp. 135–146). Springer Verlag. https://doi.org/10.1007/978-3-319-28678-5_10
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