A note on Negami's polynomial invariants for graphs (note)
Discrete Mathematics
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Splitting formulas for Tutte polynomials
Journal of Combinatorial Theory Series B
An algorithm for the Tutte polynomials of graphs of bounded treewidth
Discrete Mathematics
Colored Tutte polynomials and Kaufman brackets for graphs of bounded tree width
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
A Tutte Polynomial for Coloured Graphs
Combinatorics, Probability and Computing
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
Combinatorics, Probability and Computing
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Parametrized Tutte Polynomials of Graphs and Matroids
Combinatorics, Probability and Computing
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
An extension of the bivariate chromatic polynomial
European Journal of Combinatorics
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We observe that a formula given by Negami [Polynomial invariants of graphs, Trans. Amer. Math. Soc. 299 (1987) 601-622] for the Tutte polynomial of a k-sum of two graphs generalizes to a colored Tutte polynomial. Consequently, an algorithm of Andrzejak [An algorithm for the Tutte polynomials of graphs of bounded treewidth, Discrete Math. 190 (1998) 39-54] may be directly adapted to compute the colored Tutte polynomial of a graph of bounded treewidth in polynomial time. This result has also been proven by Makowsky [Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width, Discrete Appl. Math. 145 (2005) 276-290], using a different algorithm based on logical techniques.