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- K-tree abstract "In graph theory, a k-tree is a chordal graph all of whose maximal cliques are the same size k + 1 and all of whose minimal clique separators are also all the same size k.The k-trees are exactly the maximal graphs with a given treewidth, graphs to which no more edges can be added without increasing their treewidth. The graphs that have treewidth at most k are exactly the subgraphs of k-trees, and for this reason they are called partial k-trees.Every k-tree may be formed by starting with a (k + 1)-vertex complete graph and then repeatedly adding vertices in such a way that each added vertex has exactly k neighbors that form a clique.Certain k-trees with k ≥ 3 are also the graphs formed by the edges and vertices of stacked polytopes, polytopes formed by starting from a simplex and then repeatedly gluing simplices onto the faces of the polytope; this gluing process mimics the construction of k-trees by adding vertices to a clique. Every stacked polytope forms a k-tree in this way, but not every k-tree comes from a stacked polytope: a k-tree is the graph of a stacked polytope if and only if no three (k + 1)-vertex cliques have k vertices in common.1-trees are the same as unrooted trees. 2-trees are maximal series-parallel graphs, and include also the maximal outerplanar graphs. Planar 3-trees are also known as Apollonian networks. In higher-dimensional geometry, the stacked polytopes have graphs that are k-trees.".
- K-tree thumbnail Goldner-Harary_graph.svg?width=300.
- K-tree wikiPageID "31104438".
- K-tree wikiPageLength "4418".
- K-tree wikiPageOutDegree "23".
- K-tree wikiPageRevisionID "681977829".
- K-tree wikiPageWikiLink Apollonian_network.
- K-tree wikiPageWikiLink Category:Graph_families.
- K-tree wikiPageWikiLink Category:Graph_minor_theory.
- K-tree wikiPageWikiLink Category:Perfect_graphs.
- K-tree wikiPageWikiLink Category:Trees_(graph_theory).
- K-tree wikiPageWikiLink Chordal_graph.
- K-tree wikiPageWikiLink Clique_(graph_theory).
- K-tree wikiPageWikiLink Complete_graph.
- K-tree wikiPageWikiLink Glossary_of_graph_theory.
- K-tree wikiPageWikiLink Graph_theory.
- K-tree wikiPageWikiLink Maximal_clique.
- K-tree wikiPageWikiLink Maximal_element.
- K-tree wikiPageWikiLink Outerplanar_graph.
- K-tree wikiPageWikiLink Partial_k-tree.
- K-tree wikiPageWikiLink Planar_graph.
- K-tree wikiPageWikiLink Polytope.
- K-tree wikiPageWikiLink Series-parallel_graph.
- K-tree wikiPageWikiLink Simplex.
- K-tree wikiPageWikiLink Stacked_polytope.
- K-tree wikiPageWikiLink Tree_(graph_theory).
- K-tree wikiPageWikiLink Treewidth.
- K-tree wikiPageWikiLink File:Goldner-Harary_graph.svg.
- K-tree wikiPageWikiLinkText "''K''-trees".
- K-tree wikiPageWikiLinkText "''k''-tree".
- K-tree wikiPageWikiLinkText "''k''-trees".
- K-tree wikiPageWikiLinkText "(''d'' + 1)-tree".
- K-tree wikiPageWikiLinkText "-tree".
- K-tree wikiPageWikiLinkText "2-trees".
- K-tree wikiPageWikiLinkText "3-tree".
- K-tree wikiPageWikiLinkText "3-trees".
- K-tree wikiPageWikiLinkText "Partial ''k''-trees".
- K-tree wikiPageWikiLinkText "k-tree".
- K-tree hasPhotoCollection K-tree.
- K-tree wikiPageUsesTemplate Template:Reflist.
- K-tree subject Category:Graph_families.
- K-tree subject Category:Graph_minor_theory.
- K-tree subject Category:Perfect_graphs.
- K-tree subject Category:Trees_(graph_theory).
- K-tree hypernym Graph.
- K-tree type Software.
- K-tree type Graph.
- K-tree comment "In graph theory, a k-tree is a chordal graph all of whose maximal cliques are the same size k + 1 and all of whose minimal clique separators are also all the same size k.The k-trees are exactly the maximal graphs with a given treewidth, graphs to which no more edges can be added without increasing their treewidth.".
- K-tree label "K-tree".
- K-tree sameAs K-strom.
- K-tree sameAs m.0gh7s5m.
- K-tree sameAs Q12027616.
- K-tree sameAs Q12027616.
- K-tree wasDerivedFrom K-tree?oldid=681977829.
- K-tree depiction Goldner-Harary_graph.svg.
- K-tree isPrimaryTopicOf K-tree.