Topic
Treewidth
About: Treewidth is a research topic. Over the lifetime, 3887 publications have been published within this topic receiving 87303 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 2010
TL;DR: Fixed-Parameter Tractability.
Abstract: Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The W-Hierarchy.- The A- Hierarchy.- Kernelization and Linear Programming Techniques.- The Automata-Theoretic Approach.- Tree Width.- Planarity and Bounded Local Tree Width.- Homomorphisms and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter Tractability.- Subexponential Fixed-Parameter Tractability.- Appendix, Background from Complexity Theory.- References.- Notation.- Index.
2,733 citations
TL;DR: Every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm that determines whether the treewidth of G is at most at most some constant $k$ and finds a tree-decomposition of G withtreewidth at most k.
Abstract: In this paper, we give for constant $k$ a linear-time algorithm that, given a graph $G=(V,E)$, determines whether the treewidth of $G$ is at most $k$ and, if so, finds a tree-decomposition of $G$ with treewidth at most $k$. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant $k$.
2,039 citations
TL;DR: Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa, and the monadicsecond-order theory of a context-free set of graphs is decidable.
Abstract: The notion of a recognizable set of finite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable.
1,881 citations
TL;DR: The consecutive ones test for the consecutive ones property in matrices and for graph planarity is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs.
1,766 citations
TL;DR: This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class.
1,418 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 46 |
| 2024 | 64 |
| 2023 | 191 |
| 2022 | 263 |
| 2021 | 204 |