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- Branch-decomposition abstract "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 subgraphs formed in this way. The branchwidth of G is the minimum width of any branch-decomposition of G.Branchwidth is closely related to tree-width: for all graphs, both of these numbers are within a constant factor of each other, and both quantities may be characterized by forbidden minors. And as with treewidth, many graph optimization problems may be solved efficiently for graphs of small branchwidth. However, unlike treewidth, the branchwidth of planar graphs may be computed exactly, in polynomial time. Branch-decompositions and branchwidth may also be generalized from graphs to matroids.".
- Branch-decomposition thumbnail Branch-decomposition.svg?width=300.
- Branch-decomposition wikiPageExternalLink Branchwidth.pdf.
- Branch-decomposition wikiPageExternalLink TR00-17.ps.
- Branch-decomposition wikiPageExternalLink hal-00390623.
- Branch-decomposition wikiPageExternalLink tmerge.pdf.
- Branch-decomposition wikiPageExternalLink matr-tw-final.pdf.
- Branch-decomposition wikiPageExternalLink ICM_Vol_3_41.pdf.
- Branch-decomposition wikiPageExternalLink grid.pdf.
- Branch-decomposition wikiPageID "16823137".
- Branch-decomposition wikiPageLength "20271".
- Branch-decomposition wikiPageOutDegree "59".
- Branch-decomposition wikiPageRevisionID "680553090".
- Branch-decomposition wikiPageWikiLink Biconnected_component.
- Branch-decomposition wikiPageWikiLink Category:Graph_invariants.
- Branch-decomposition wikiPageWikiLink Category:Graph_minor_theory.
- Branch-decomposition wikiPageWikiLink Category:Matroid_theory.
- Branch-decomposition wikiPageWikiLink Category:Trees_(graph_theory).
- Branch-decomposition wikiPageWikiLink Complete_graph.
- Branch-decomposition wikiPageWikiLink Connected_component_(graph_theory).
- Branch-decomposition wikiPageWikiLink Dual_matroid.
- Branch-decomposition wikiPageWikiLink Dynamic_programming.
- Branch-decomposition wikiPageWikiLink Finite_field.
- Branch-decomposition wikiPageWikiLink Forbidden_graph_characterization.
- Branch-decomposition wikiPageWikiLink Forbidden_minor.
- Branch-decomposition wikiPageWikiLink Graph_(mathematics).
- Branch-decomposition wikiPageWikiLink Graph_minor.
- Branch-decomposition wikiPageWikiLink Graph_theory.
- Branch-decomposition wikiPageWikiLink Graphic_matroid.
- Branch-decomposition wikiPageWikiLink Hierarchical_clustering.
- Branch-decomposition wikiPageWikiLink Hypercube_graph.
- Branch-decomposition wikiPageWikiLink International_Congress_of_Mathematicians.
- Branch-decomposition wikiPageWikiLink Journal_of_Combinatorial_Theory.
- Branch-decomposition wikiPageWikiLink Matching_(graph_theory).
- Branch-decomposition wikiPageWikiLink Matroid.
- Branch-decomposition wikiPageWikiLink Matroid_minor.
- Branch-decomposition wikiPageWikiLink Matroid_oracle.
- Branch-decomposition wikiPageWikiLink Matroid_rank.
- Branch-decomposition wikiPageWikiLink Medial_graph.
- Branch-decomposition wikiPageWikiLink Minor_(graph_theory).
- Branch-decomposition wikiPageWikiLink NP-complete.
- Branch-decomposition wikiPageWikiLink NP-completeness.
- Branch-decomposition wikiPageWikiLink Neil_Robertson_(mathematician).
- Branch-decomposition wikiPageWikiLink Octahedron.
- Branch-decomposition wikiPageWikiLink Parameterized_complexity.
- Branch-decomposition wikiPageWikiLink Path_graph.
- Branch-decomposition wikiPageWikiLink Paul_Seymour_(mathematician).
- Branch-decomposition wikiPageWikiLink Planar_graph.
- Branch-decomposition wikiPageWikiLink Planar_graphs.
- Branch-decomposition wikiPageWikiLink Polynomial_time.
- Branch-decomposition wikiPageWikiLink Robertson–Seymour_theorem.
- Branch-decomposition wikiPageWikiLink Robin_Thomas_(mathematician).
- Branch-decomposition wikiPageWikiLink Series-parallel_graph.
- Branch-decomposition wikiPageWikiLink Spectral_clustering.
- Branch-decomposition wikiPageWikiLink Star_(graph_theory).
- Branch-decomposition wikiPageWikiLink Time_complexity.
- Branch-decomposition wikiPageWikiLink Travelling_salesman_problem.
- Branch-decomposition wikiPageWikiLink Tree_decomposition.
- Branch-decomposition wikiPageWikiLink Treewidth.
- Branch-decomposition wikiPageWikiLink Undirected_graph.
- Branch-decomposition wikiPageWikiLink Uniform_matroid.
- Branch-decomposition wikiPageWikiLink Unrooted_binary_tree.
- Branch-decomposition wikiPageWikiLink Wagner_graph.
- Branch-decomposition wikiPageWikiLink Well-quasi-ordering.
- Branch-decomposition wikiPageWikiLink File:Branch-decomposition.svg.
- Branch-decomposition wikiPageWikiLink File:Branchwidth_3-forbidden_minors.svg.
- Branch-decomposition wikiPageWikiLinkText "Branch-decomposition".
- Branch-decomposition wikiPageWikiLinkText "branch-decomposition".
- Branch-decomposition hasPhotoCollection Branch-decomposition.
- Branch-decomposition wikiPageUsesTemplate Template:Citation.
- Branch-decomposition wikiPageUsesTemplate Template:Commons_category.
- Branch-decomposition wikiPageUsesTemplate Template:Harvtxt.
- Branch-decomposition wikiPageUsesTemplate Template:Refbegin.
- Branch-decomposition wikiPageUsesTemplate Template:Refend.
- Branch-decomposition wikiPageUsesTemplate Template:Reflist.
- Branch-decomposition wikiPageUsesTemplate Template:Sfnp.
- Branch-decomposition subject Category:Graph_invariants.
- Branch-decomposition subject Category:Graph_minor_theory.
- Branch-decomposition subject Category:Matroid_theory.
- Branch-decomposition subject Category:Trees_(graph_theory).
- Branch-decomposition type Combinatoric.
- Branch-decomposition type Invariant.
- Branch-decomposition type Object.
- Branch-decomposition comment "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 subgraphs formed in this way.".
- Branch-decomposition label "Branch-decomposition".
- Branch-decomposition sameAs Κλαδοπλάτος.
- Branch-decomposition sameAs m.0407hs5.
- Branch-decomposition sameAs Q4956329.
- Branch-decomposition sameAs Q4956329.
- Branch-decomposition wasDerivedFrom Branch-decomposition?oldid=680553090.
- Branch-decomposition depiction Branch-decomposition.svg.
- Branch-decomposition isPrimaryTopicOf Branch-decomposition.