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Branch-decomposition

In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges of G as its leaves. Removing any edge from T partitions the edges of G into two subgraphs, and the width of the decomposition is the maximum number of shared vertices of any pair of…

Art, Forbidden minors & Algorithms and complexity

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Overview

Definitions

Relation to treewidth

Carving width

Algorithms and complexity

Generalization to matroids

Forbidden minors

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Map overview Semantic statistics

Branch-decomposition

Nodes58
Edges57
Triples32
Avg. degree1.97
Density0.034483
Components1

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Branch-decomposition

Top relations

related to Definitions · 10
Branch-decomposition → An, E1, E2, G1, G2, If, T1, T2, The, This
related to Generalization to matroids · 9
Branch-decomposition → Additionally, An, Branchwidth, However, If, It, Robertson, Seymour, The
related to Algorithms and complexity · 8
Branch-decomposition → For, However, It, NP-complete, Paul Seymour, Robin Thomas, The, This
related to Relation to treewidth · 4
Branch-decomposition → Branch-decompositions, In, Neil Robertson, Paul Seymour
is a · 1
Branch-decomposition → maximum width of any of its e-separations

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Important terminology

branchwidth graph graphs width treewidth forbidden matroid may matroids minors tree two planar time edges minimal seymour unrooted binary decomposition

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Branch-decompositionis amaximum width of any of its e-separations0.90text
Branch-decompositionrelated to Algorithms and complexityIt0.60section
Branch-decompositionrelated to Algorithms and complexityNP-complete0.60section
Branch-decompositionrelated to Algorithms and complexityHowever0.60section
Branch-decompositionrelated to Algorithms and complexityFor0.60section
Branch-decompositionrelated to Algorithms and complexityThis0.60section
Branch-decompositionrelated to Algorithms and complexityThe0.60section
Branch-decompositionrelated to Algorithms and complexityPaul Seymour0.60section
Branch-decompositionrelated to Algorithms and complexityRobin Thomas0.60section
Branch-decompositionrelated to DefinitionsAn0.60section
Branch-decompositionrelated to DefinitionsIf0.60section
Branch-decompositionrelated to DefinitionsT10.60section

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