ALCOMFT-TR-01-142

J. D\'\iaz, M. Serna and D. M. Thilikos
Counting H-colorings of Partial k-trees
Barcelona. Work package 4. June 2001.

Abstract: The problem of counting all H-colorings of a graph G of n vertices is considered. While the problem, in general, is #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.

Postscript file: ALCOMFT-TR-01-142.ps.gz (124 kb).