Counting H-colorings of partial k-trees

Josep Dìaz, Maria Serna, Dimitrios M. Thilikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationComputing and Combinatorics - 7th Annual International Conference, COCOON 2001, Proceedings
EditorsJie Wang
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783540424949
StatePublished - 2001
Event7th Annual International Conference on Computing and Combinatorics, COCOON 2001 - Guilin, China
Duration: Aug 20 2001Aug 23 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th Annual International Conference on Computing and Combinatorics, COCOON 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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