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- Clique_complex abstract "“Whitney complex” redirects here. For the Mississippi sports facility, see Davey Whitney Complex.Clique complexes, flag complexes, and conformal hypergraphs are closely related mathematical objects in graph theory and geometric topology that each describe the cliques (complete subgraphs) of an undirected graph.The clique complex X(G) of an undirected graph G is an abstract simplicial complex (that is, a family of finite sets closed under the operation of taking subsets), formed by the sets of vertices in the cliques of G. Any subset of a clique is itself a clique, so this family of sets meets the requirement of an abstract simplicial complex that every subset of a set in the family should also be in the family. The clique complex can also be viewed as a topological space in which each clique of k vertices is represented by a simplex of dimension k − 1. The 1-skeleton of X(G) (also known as the underlying graph of the complex) is an undirected graph with a vertex for every 1-element set in the family and an edge for every 2-element set in the family; it is isomorphic to G.Clique complexes are also known as Whitney complexes. A Whitney triangulation or clean triangulation of a two-dimensional manifold is an embedding of a graph G onto the manifold in such a way that every face is a triangle and every triangle is a face. If a graph G has a Whitney triangulation, it must form a cell complex that is isomorphic to the Whitney complex of G. In this case, the complex (viewed as a topological space) is homeomorphic to the underlying manifold. A graph G has a 2-manifold clique complex, and can be embedded as a Whitney triangulation, if and only if G is locally cyclic; this means that, for every vertex v in the graph, the induced subgraph formed by the neighbors of v forms a single cycle.".
- Clique_complex thumbnail VR_complex.svg?width=300.
- Clique_complex wikiPageExternalLink survey_cm_bis.pdf.
- Clique_complex wikiPageExternalLink v9i1r17.html.
- Clique_complex wikiPageExternalLink cuello10_DM.ps.
- Clique_complex wikiPageID "20751674".
- Clique_complex wikiPageLength "10799".
- Clique_complex wikiPageOutDegree "51".
- Clique_complex wikiPageRevisionID "652127271".
- Clique_complex wikiPageWikiLink Abstract_simplicial_complex.
- Clique_complex wikiPageWikiLink Barycentric_subdivision.
- Clique_complex wikiPageWikiLink CAT(k)_space.
- Clique_complex wikiPageWikiLink CW_complex.
- Clique_complex wikiPageWikiLink Category:Algebraic_topology.
- Clique_complex wikiPageWikiLink Category:Hypergraphs.
- Clique_complex wikiPageWikiLink Category:Set_families.
- Clique_complex wikiPageWikiLink Chessboard_complex.
- Clique_complex wikiPageWikiLink Clique_(graph_theory).
- Clique_complex wikiPageWikiLink Comparability_graph.
- Clique_complex wikiPageWikiLink Complement_graph.
- Clique_complex wikiPageWikiLink Complete_bipartite_graph.
- Clique_complex wikiPageWikiLink Complete_graph.
- Clique_complex wikiPageWikiLink Constraint_graph.
- Clique_complex wikiPageWikiLink Cubing_(topology).
- Clique_complex wikiPageWikiLink Davey_Whitney_Complex.
- Clique_complex wikiPageWikiLink Discrete_Mathematics_(journal).
- Clique_complex wikiPageWikiLink Flag_(geometry).
- Clique_complex wikiPageWikiLink Geometric_topology.
- Clique_complex wikiPageWikiLink Glossary_of_graph_theory.
- Clique_complex wikiPageWikiLink Graph_(mathematics).
- Clique_complex wikiPageWikiLink Graph_embedding.
- Clique_complex wikiPageWikiLink Graph_theory.
- Clique_complex wikiPageWikiLink Guarded_logic.
- Clique_complex wikiPageWikiLink Homeomorphism.
- Clique_complex wikiPageWikiLink Hypercube.
- Clique_complex wikiPageWikiLink Hypercubes.
- Clique_complex wikiPageWikiLink Hypergraph.
- Clique_complex wikiPageWikiLink Independent_set_(graph_theory).
- Clique_complex wikiPageWikiLink Induced_subgraph.
- Clique_complex wikiPageWikiLink Line_graph.
- Clique_complex wikiPageWikiLink Manifold.
- Clique_complex wikiPageWikiLink Matching_complex.
- Clique_complex wikiPageWikiLink Mathematics.
- Clique_complex wikiPageWikiLink Matroid.
- Clique_complex wikiPageWikiLink Matroid_intersection.
- Clique_complex wikiPageWikiLink Mikhail_Leonidovich_Gromov.
- Clique_complex wikiPageWikiLink N-skeleton.
- Clique_complex wikiPageWikiLink Neighbourhood_(graph_theory).
- Clique_complex wikiPageWikiLink Order_complex.
- Clique_complex wikiPageWikiLink Partially_ordered_set.
- Clique_complex wikiPageWikiLink Partition_matroid.
- Clique_complex wikiPageWikiLink Poset_topology.
- Clique_complex wikiPageWikiLink Pseudo-manifold.
- Clique_complex wikiPageWikiLink Pseudomanifold.
- Clique_complex wikiPageWikiLink Rooks_graph.
- Clique_complex wikiPageWikiLink Shortest_path.
- Clique_complex wikiPageWikiLink Shortest_path_problem.
- Clique_complex wikiPageWikiLink Simplex.
- Clique_complex wikiPageWikiLink Simplex_graph.
- Clique_complex wikiPageWikiLink Total_order.
- Clique_complex wikiPageWikiLink Triangulation_(topology).
- Clique_complex wikiPageWikiLink Undirected_graph.
- Clique_complex wikiPageWikiLink Unit_disk_graph.
- Clique_complex wikiPageWikiLink Vietoris–Rips_complex.
- Clique_complex wikiPageWikiLink File:VR_complex.svg.
- Clique_complex wikiPageWikiLinkText "Clique complex".
- Clique_complex wikiPageWikiLinkText "clique complex".
- Clique_complex wikiPageWikiLinkText "independence complex".
- Clique_complex hasPhotoCollection Clique_complex.
- Clique_complex wikiPageUsesTemplate Template:Citation.
- Clique_complex wikiPageUsesTemplate Template:Harvtxt.
- Clique_complex wikiPageUsesTemplate Template:Reflist.
- Clique_complex subject Category:Algebraic_topology.
- Clique_complex subject Category:Hypergraphs.
- Clique_complex subject Category:Set_families.
- Clique_complex type Combinatoric.
- Clique_complex type Concept.
- Clique_complex comment "“Whitney complex” redirects here.".
- Clique_complex label "Clique complex".
- Clique_complex sameAs Fahnenkomplex.
- Clique_complex sameAs m.058vch5.
- Clique_complex sameAs Q5134413.
- Clique_complex sameAs Q5134413.
- Clique_complex wasDerivedFrom Clique_complex?oldid=652127271.
- Clique_complex depiction VR_complex.svg.
- Clique_complex isPrimaryTopicOf Clique_complex.