Counting H-colorings of partial k-trees

Josep Díaz, Maria Serna, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


The problem of counting all H-colorings of a graph G with 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.

Original languageEnglish (US)
Pages (from-to)291-309
Number of pages19
JournalTheoretical Computer Science
Issue number1-2
StatePublished - Jun 3 2002


  • Counting problems
  • Graph homomorphism
  • Treewidth

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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