The problem of counting all H-colorings of a graph G of n vertices is considered. While the problem is, in general, #P-complete, we give linear time algorithms that solve the main variants of this problem when the input graph G is a k-tree or, in the case where G is directed, when the underlying graph of G is a k-tree. Our algorithms remain polynomial even in the case where k = O(log n) or in the case where the size of H is O(n). Our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial k-trees such as core checking and chromatic polynomial computation.
CITATION STYLE
Dìaz, J., Serna, M., & Thilikos, D. M. (2001). Counting H-colorings of partial k-trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2108, pp. 298–307). Springer Verlag. https://doi.org/10.1007/3-540-44679-6_33
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