Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Handbook of combinatorics (vol. 1)
Two algorithmic results for the traveling salesman problem
Mathematics of Operations Research
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Journal of Combinatorial Theory Series B
NC-Algorithms for Graphs with Small Treewidth
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
On the expressive power of planar perfect matching and permanents of bounded treewidth matrices
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
On the expressive power of CNF formulas of bounded tree- and clique-width
Discrete Applied Mathematics
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It is well known that permanents of matrices of bounded treewidth are efficiently computable. Here, the tree-width of a square matrix M = (mij) with entries from a field K is the tree-width of the underlying graph GM having an edge (i, j) if and only if the entry mij ≠ 0. Though GM is directed this does not influence the tree-width definition. Thus, it does not reflect the lacking symmetry when mij ≠ 0 but mji = 0. The latter however might have impact on the computation of the permanent. In this paper we introduce and study an extended notion of tree-width called triangular tree-width. We give examples where the latter parameter is bounded whereas the former is not. As main result we show that permanents of matrices of bounded triangular tree-width are efficiently computable. This result holds as well for the Hamiltonian Cycle problem.