Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
The complexity of colouring problems on dense graphs
Theoretical Computer Science
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Generalized coloring for tree-like graphs
Discrete Applied Mathematics
An algorithm for the Tutte polynomials of graphs of bounded treewidth
Discrete Mathematics
On Approximately Counting Colorings of Small Degree Graphs
SIAM Journal on Computing
The complexity of counting graph homomorphisms (extended abstract)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The complexity of H-colouring of bounded degree graphs
Discrete Mathematics
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
On Markov chains for randomly H-coloring a graph
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
On Counting Independent Sets in Sparse Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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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.