Abstract
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.
Research supported by the EU project ALCOM-FT (IST-99-14186). The research of the 3rd author was supported by the Ministry of Education and Culture of Spain, Grant number MEC-DGES SB98 0K148809.
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Díaz, J., Serna, M., Thilikos, D.M. (2001). Counting H-Colorings of Partial k-Trees. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_33
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