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- Combinatorial_map abstract "A combinatorial map is a combinatorial object modelling topological structures with subdivided objects. Historically, the concept was introduced informally by J. Edmonds for polyhedral surfaces which are planar graphs. It was given its first definite formal expression under the name "Constellations" by A. Jacques but the concept was already extensively used under the name "rotation" by Gerhard Ringel and J.W.T. Youngs in their famous solution of the Heawood map-coloring problem. The term "constellation" was not retained and instead "combinatorial map" was favored. The concept was later extended to represent higher-dimensional orientable subdivided objects. Combinatorial maps are used as efficient data structures in image representation and processing, in geometrical modeling. This model is related to simplicial complexes and to combinatorial topology. Note that combinatorial maps were extended to generalized maps that allow also to represent non-orientable objects like the Möbius strip and the Klein bottle. A combinatorial map is a boundary representation model; it represents object by its boundaries.".
- Combinatorial_map thumbnail Combinatorial_map_planar_graph_example.svg?width=300.
- Combinatorial_map wikiPageExternalLink CombinatorialMaps.
- Combinatorial_map wikiPageExternalLink cgogn.unistra.fr.
- Combinatorial_map wikiPageID "21105530".
- Combinatorial_map wikiPageLength "7314".
- Combinatorial_map wikiPageOutDegree "32".
- Combinatorial_map wikiPageRevisionID "627385087".
- Combinatorial_map wikiPageWikiLink Boundary_representation.
- Combinatorial_map wikiPageWikiLink CGAL.
- Combinatorial_map wikiPageWikiLink Category:Algebraic_topology.
- Combinatorial_map wikiPageWikiLink Category:Computer_graphics_data_structures.
- Combinatorial_map wikiPageWikiLink Category:Graph_data_structures.
- Combinatorial_map wikiPageWikiLink Category:Topological_graph_theory.
- Combinatorial_map wikiPageWikiLink Combinatorial_topology.
- Combinatorial_map wikiPageWikiLink Combinatorics.
- Combinatorial_map wikiPageWikiLink File:Combinatorial_map_dual_example.svg.
- Combinatorial_map wikiPageWikiLink File:Combinatorial_map_example.svg.
- Combinatorial_map wikiPageWikiLink File:Combinatorial_map_planar_graph_example.svg.
- Combinatorial_map wikiPageWikiLink Generalized_map.
- Combinatorial_map wikiPageWikiLink Generalized_maps.
- Combinatorial_map wikiPageWikiLink Gerhard_Ringel.
- Combinatorial_map wikiPageWikiLink Image_processing.
- Combinatorial_map wikiPageWikiLink Involution_(mathematics).
- Combinatorial_map wikiPageWikiLink Klein_bottle.
- Combinatorial_map wikiPageWikiLink Möbius_strip.
- Combinatorial_map wikiPageWikiLink Permutation.
- Combinatorial_map wikiPageWikiLink Planar_graph.
- Combinatorial_map wikiPageWikiLink Polyhedral_surface.
- Combinatorial_map wikiPageWikiLink Polyhedron.
- Combinatorial_map wikiPageWikiLink Quad-edge.
- Combinatorial_map wikiPageWikiLink Quad-edge_data_structure.
- Combinatorial_map wikiPageWikiLink Rotation_system.
- Combinatorial_map wikiPageWikiLink Simplicial_complex.
- Combinatorial_map wikiPageWikiLink Topology.
- Combinatorial_map wikiPageWikiLink Winged_edge.
- Combinatorial_map wikiPageWikiLinkText "Combinatorial map".
- Combinatorial_map wikiPageWikiLinkText "combinatorial map".
- Combinatorial_map hasPhotoCollection Combinatorial_map.
- Combinatorial_map wikiPageUsesTemplate Template:Cite_web.
- Combinatorial_map subject Category:Algebraic_topology.
- Combinatorial_map subject Category:Computer_graphics_data_structures.
- Combinatorial_map subject Category:Graph_data_structures.
- Combinatorial_map subject Category:Topological_graph_theory.
- Combinatorial_map hypernym Object.
- Combinatorial_map type Planet.
- Combinatorial_map type Object.
- Combinatorial_map type Structure.
- Combinatorial_map comment "A combinatorial map is a combinatorial object modelling topological structures with subdivided objects. Historically, the concept was introduced informally by J. Edmonds for polyhedral surfaces which are planar graphs. It was given its first definite formal expression under the name "Constellations" by A. Jacques but the concept was already extensively used under the name "rotation" by Gerhard Ringel and J.W.T. Youngs in their famous solution of the Heawood map-coloring problem.".
- Combinatorial_map label "Combinatorial map".
- Combinatorial_map sameAs Carte_combinatoire.
- Combinatorial_map sameAs m.05bz_9p.
- Combinatorial_map sameAs Q2940480.
- Combinatorial_map sameAs Q2940480.
- Combinatorial_map wasDerivedFrom Combinatorial_map?oldid=627385087.
- Combinatorial_map depiction Combinatorial_map_planar_graph_example.svg.
- Combinatorial_map isPrimaryTopicOf Combinatorial_map.