Enumerative combinatorics
Generating functionology
Discrete Mathematics
Easy problems for tree-decomposable graphs
Journal of Algorithms
The monadic second-order logic of graphs VII: graphs as relational structures
Theoretical Computer Science - Special issue on logic and applications to computer science
Model theory and computer science: an appetizer
Handbook of logic in computer science (vol. 1)
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Clique polynomials and independent set polynomials of graphs
Selected papers of the 13th British Combinatorial Conference on British combinatorial conference
An algorithm for the Tutte polynomials of graphs of bounded treewidth
Discrete Mathematics
New results for the Martin polynomial
Journal of Combinatorial Theory Series B
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
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Graph Algorithms
Uniform definability on finite structures with successor
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
The parametrized complexity of knot polynomials
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
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)
The parametrized complexity of knot polynomials
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Linear recurrence relations for graph polynomials
Pillars of computer science
Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
From a zoo to a zoology: descriptive complexity for graph polynomials
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Almost linear time computation of the chromatic polynomial of a graph of bounded tree-width
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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We consider various classes of graph polynomials and study their computational complexity. Our main focus is on Farrell polynomials and generating functions of graph properties. All these polynomials have a wide range of applications in combinatorics, but also in physics, chemistry, and biology. In general, the worst-case complexity of most these polynomials is known to be NP-hard. or even #P-hard. We show that, if these polynomials satisfy a definability condition in the formalisms of monadic second-order logic, then they can be computed in polynomial time if restricted to graphs of tree width at most k. In other words, they are fixed-parameter tractable (FPT) with parameter the tree width of the input graph.