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Everything about Twin-width
The twin-width of an undirected graph is a natural number associated with the graph, used to study the parameterized complexity of graph algorithms. Intuitively, it measures how similar the graph is to a cograph, a type of graph that can be reduced to a single vertex by repeatedly merging together twins, vertices that have the same neighbors. The twin-width is defined from a sequence of repeated mergers where the vertices are not required to be twins, but have nearly equal sets of neighbors. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Twin-widthA 5-minute orientation
- Skim a recent paper: Bounds for the Twin-Width of GraphsInfluential work since 2022
- Pick up a classic book: Intelligence BulletinThe most-reprinted book on the subject
- Read the landmark paper: Effects of gap width on flow motions around twin-box girders and vortex-induced vibrationsCited 90 times
- Go sideways: Laman graphA closely related topic
- Go sideways: Clique-widthA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Effects of gap width on flow motions around twin-box girders and vortex-induced vibrations
Twin-width I: Tractable FO Model Checking
Effective Slab Width in Prestressed Twin-Girder Composite Decks
Influence of gap width on buffeting force spatial correlation and aerodynamic admittance of twin-box bridge deck
STM revealing of twin microlayers with quantized width on cleaved bismuth surface
Twin-width and Polynomial Kernels
Twin-Width IV: Ordered Graphs and Matrices
Tailor Blank Casting—Control of sheet width using an electromagnetic edge dam in aluminium twin roll casting
🆕 Influential since 2022
📚 Books worth reading
Intelligence BulletinUnited States. War Department. Military Intelligence Service · 1942
Exploratory data analysisJohn Wilder Tukey · 1970- 📕Comparison of maxillary and mandibular anterior deciduous tooth widths in monozygotic and dizygotic twinsCecil Alumbaugh · 1972
- 📕The impatient managerWalter Vieira · 2016
Analog Circuit DesignPeter D. Hiscocks · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Laman graph In graph theory, the Laman graphs are a family of sparse graphs describing the minimally rigid systems of rods and joints in the plane. Formally, a Laman…
- Clique-width In graph theory, the clique-width of a graph G is a parameter that describes the structural complexity of the graph; it is closely related to treewidth…
- Metric dimension (graph theory) In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely determined…
- Parameterized approximation algorithm A parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial time…
- Contraction hierarchies In computer science, the method of contraction hierarchies is a speed-up technique for finding the shortest path in a graph. The most intuitive applications…
- Strong product of graphs In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they…
- Distance-hereditary graph In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances…
- Cograph In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation…