Journal of Combinatorial Theory Series B
Easy problems for tree-decomposable graphs
Journal of Algorithms
Approximating the permanent of graphs with large factors
Theoretical Computer Science
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Counting the number of independent sets in chordal graphs
Journal of Discrete Algorithms
Counting the Number of Matchings in Chordal and Chordal Bipartite Graph Classes
Graph-Theoretic Concepts in Computer Science
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Computing graph polynomials on graphs of bounded clique-width
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Computing the tutte polynomial on graphs of bounded clique-width
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
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In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal matchings, we introduce matchingcover pairs to efficiently handle maximality in the local structure, and develop a polynomial time algorithm. For path matchings, we develop a way to classify the path matchings in a polynomial number of equivalent classes. Using these, we develop dynamic programing algorithms that run in polynomial time of the graph size, but in exponential time of the clique-width. In particular, we show that for a graph G of n vertices and clique-width k, these problems can be solved in O(nf(k)) time where f is exponential in k or in O(ng(l)) time where g is linear or quadratic in l if an l-expression for G is given as input.