Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. VI. Disjoint paths across a disc
Journal of Combinatorial Theory Series B
Characterization and recognition of partial 3-trees
SIAM Journal on Algebraic and Discrete Methods
Linear-time computation of optimal subgraphs of decomposable graphs
Journal of Algorithms
Parallel recognition and decomposition of two terminal series parallel graphs
Information and Computation
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Graph minors. VII. Disjoint paths on a surface
Journal of Combinatorial Theory Series B
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Graph minors. IX. Disjoint crossed paths
Journal of Combinatorial Theory Series B
Graph minors. IV. Tree-width and well-quasi-ordering
Journal of Combinatorial Theory Series B
Graph minors. VIII. A Kuratowski theorem for general surfaces
Journal of Combinatorial Theory Series B
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Forbidden minors characterization of partial 3-trees
Discrete Mathematics
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Easy problems for tree-decomposable graphs
Journal of Algorithms
Algorithms finding tree-decompositions of graphs
Journal of Algorithms
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
Deterministic decomposition of recursive graph classes
SIAM Journal on Discrete Mathematics
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
Monadic second-order evaluations on tree-decomposable graphs
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Efficient sets in partial k-trees
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Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
An algebraic theory of graph reduction
Journal of the ACM (JACM)
Handle-rewriting hypergraph grammars
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Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Graph minors. XI.: circuits on a surface
Journal of Combinatorial Theory Series B
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Linear algorithms for graphs of tree-width at most four
Linear algorithms for graphs of tree-width at most four
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Linear time optimization for P 4-sparse graphs
Discrete Applied Mathematics
Treewidth of chordal bipartite graphs
Journal of Algorithms
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
The monadic second-order logic of graphs X: linear orderings
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On Linear Recognition of Tree-Width at Most Four
SIAM Journal on Discrete Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Journal of Algorithms
On the structure of graphs with few P4s
Discrete Applied Mathematics
All structured programs have small tree width and good register allocation
Information and Computation
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Graph classes: a survey
Linear-time register allocation for a fixed number of registers
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Make it practical: a generic linear-time algorithm for solving maximum-weightsum problems
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
A practical algorithm for making filled graphs minimal
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A sufficiently fast algorithm for finding close to optimal clique trees
Artificial Intelligence
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Algorithms for generalized vertex-rankings of partial k-trees
Theoretical Computer Science - computing and combinatorics
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
A combinatorial and logical approach to linear-time computability
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Efficient Approximation for Triangulation of Minimum Treewidth
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How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
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Mona & Fido: The Logic-Automaton Connection in Practice
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
A Linear Algorithm for Edge-Coloring Partial k-Trees
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
A New Lower Bound for Tree-Width Using Maximum Cardinality Search
SIAM Journal on Discrete Mathematics
Combinatorial optimization on series-parallel graphs: algorithms and complexity
Combinatorial optimization on series-parallel graphs: algorithms and complexity
Linear algorithms on k-terminal graphs
Linear algorithms on k-terminal graphs
Recursively constructed graph families: membership and linear algorithms
Recursively constructed graph families: membership and linear algorithms
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
A complete anytime algorithm for treewidth
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Improved approximation algorithms for minimum-weight vertex separators
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On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Graphs of bounded rank-width
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Vertex disjoint paths on clique-width bounded graphs
Theoretical Computer Science
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
New lower and upper bounds for graph treewidth
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient 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
A branch and bound algorithm for exact, upper, and lower bounds on treewidth
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Approximating rank-width and clique-width quickly
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NP-hard graph problems and boundary classes of graphs
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Algorithms and theory of computation handbook
Boundary properties of graphs for algorithmic graph problems
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On prime inductive classes of graphs
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Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Probabilistic inference and monadic second order logic
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
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Fast algorithms can be created for many graph problems when instances are confined to classes of graphs that are recursively constructed. This article first describes some basic conceptual notions regarding the design of such fast algorithms, and then the coverage proceeds through several recursive graph classes. Specific classes include trees, series-parallel graphs, k-terminal graphs, treewidth-k graphs, k-trees, partial k-trees, k-jackknife graphs, pathwidth-k graphs, bandwidth-k graphs, cutwidth-k graphs, branchwidth-k graphs, Halin graphs, cographs, cliquewidth-k graphs, k-NLC graphs, k-HB graphs, and rankwidth-k graphs. The definition of each class is provided. Typical algorithms are applied to solve problems on instances of most classes. Relationships between the classes are also discussed.