Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
A Tutte polynomial for signed graphs
Discrete Applied Mathematics - Combinatorics and complexity
Calculating the 2-variable polynomial for knots presented as closed braids
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
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
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
The computational complexity of knot and link problems
Journal of the ACM (JACM)
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
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Farrell polynomials on graphs of bounded tree width
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Fusion in relational structures and the verification of monadic second-order properties
Mathematical Structures in Computer Science
Farrell polynomials on graphs of bounded tree width
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
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
Computing HOMFLY polynomials of 2-bridge links from 4-plat representation
Discrete Applied Mathematics
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We study the parametrized complexity of the knot (and link) polynomials known as Jones polynomials, Kauffman polynomials and HOMFLY polynomials. It is known that computing these polynomials is #P hard in general. We look for parameters of the combinatorial presentation of knots and links which make the computation of these polynomials to be fixed parameter tractable, i.e., in the complexity class FPT. If the link is explicitly presented as a closed braid, the number of its strands is known to be such a parameter. In a generalization thereof, if the link is explicitly presented as a combination of compositions and rotations of k-tangles the link is called k-algebraic, and its algebraicity k is such a parameter. The previously known proofs that, for this parameter, the link polynomials are in FPT uses the so called skein modules, and is algebraic in its nature. Furthermore, it is not clear how to find such an algebraic presentation from a given link diagram. We look at the treewidth of two combinatorial presentation of links: the crossing diagram and its shading diagram, a signed graph. We show that the treewidth of these two presentations and the algebraicity of links are all linearly related to each other. Furthermore, we characterize the k-algebraic links using the pathwidth of the crossing diagram. Using this, we can apply algorithms for testing fixed treewidth to find k-algebraic presentations in polynomial time. From this we can conclude that also treewidth and pathwidth are parameters of link diagrams for which the knot polynomials are FPT. For the Kauffman and Jones polynomials (but not for the HOMFLY polynomials) we get also a different proof for FPT via the corresponding result for signed Tutte polynomials.