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- Zarankiewicz_problem abstract "The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices but has no complete bipartite subgraphs of a given size. It belongs to the field of extremal graph theory, a branch of combinatorics, and is named after the Polish mathematician Kazimierz Zarankiewicz, who proposed several special cases of the problem in 1951.The Kővári–Sós–Turán theorem, named after Tamás Kővári, Vera T. Sós, and Pál Turán, provides an upper bound on the solution to the Zarankiewicz problem. When the forbidden complete bipartite subgraph has one side with at most three vertices, this bound has been proven to be within a constant factor of the correct answer. For larger forbidden subgraphs, it remains the best known bound, and has been conjectured to be tight. Applications of the Kővári–Sós–Turán theorem include bounding the number of incidences between different types of geometric object in discrete geometry.".
- Zarankiewicz_problem thumbnail Zarankiewicz-4-3.svg?width=300.
- Zarankiewicz_problem wikiPageID "3480707".
- Zarankiewicz_problem wikiPageLength "15146".
- Zarankiewicz_problem wikiPageOutDegree "48".
- Zarankiewicz_problem wikiPageRevisionID "702194713".
- Zarankiewicz_problem wikiPageWikiLink Asymptotic_analysis.
- Zarankiewicz_problem wikiPageWikiLink Biclique-free_graph.
- Zarankiewicz_problem wikiPageWikiLink Big_O_notation.
- Zarankiewicz_problem wikiPageWikiLink Bipartite_double_cover.
- Zarankiewicz_problem wikiPageWikiLink Bipartite_graph.
- Zarankiewicz_problem wikiPageWikiLink Cage_(graph_theory).
- Zarankiewicz_problem wikiPageWikiLink Category:Extremal_graph_theory.
- Zarankiewicz_problem wikiPageWikiLink Category:Mathematical_problems.
- Zarankiewicz_problem wikiPageWikiLink Category:Unsolved_problems_in_mathematics.
- Zarankiewicz_problem wikiPageWikiLink Combinatorics.
- Zarankiewicz_problem wikiPageWikiLink Complete_bipartite_graph.
- Zarankiewicz_problem wikiPageWikiLink Cube.
- Zarankiewicz_problem wikiPageWikiLink Degree_(graph_theory).
- Zarankiewicz_problem wikiPageWikiLink Digital_geometry.
- Zarankiewicz_problem wikiPageWikiLink Discrete_geometry.
- Zarankiewicz_problem wikiPageWikiLink Extremal_graph_theory.
- Zarankiewicz_problem wikiPageWikiLink Fano_plane.
- Zarankiewicz_problem wikiPageWikiLink Finite_geometry.
- Zarankiewicz_problem wikiPageWikiLink Forbidden_graph_characterization.
- Zarankiewicz_problem wikiPageWikiLink Forbidden_subgraph_problem.
- Zarankiewicz_problem wikiPageWikiLink Girth_(graph_theory).
- Zarankiewicz_problem wikiPageWikiLink Graph_(discrete_mathematics).
- Zarankiewicz_problem wikiPageWikiLink Heawood_graph.
- Zarankiewicz_problem wikiPageWikiLink Hexagon.
- Zarankiewicz_problem wikiPageWikiLink Induced_subgraph.
- Zarankiewicz_problem wikiPageWikiLink Integer_lattice.
- Zarankiewicz_problem wikiPageWikiLink Kazimierz_Zarankiewicz.
- Zarankiewicz_problem wikiPageWikiLink Levi_graph.
- Zarankiewicz_problem wikiPageWikiLink Logical_matrix.
- Zarankiewicz_problem wikiPageWikiLink Matrix_(mathematics).
- Zarankiewicz_problem wikiPageWikiLink Matrix_of_ones.
- Zarankiewicz_problem wikiPageWikiLink Projective_plane.
- Zarankiewicz_problem wikiPageWikiLink Pál_Turán.
- Zarankiewicz_problem wikiPageWikiLink Szemerédi–Trotter_theorem.
- Zarankiewicz_problem wikiPageWikiLink Turxc3xa1ns_theorem.
- Zarankiewicz_problem wikiPageWikiLink Two-dimensional_space.
- Zarankiewicz_problem wikiPageWikiLink Upper_and_lower_bounds.
- Zarankiewicz_problem wikiPageWikiLink Vera_T._Sós.
- Zarankiewicz_problem wikiPageWikiLink Vertex_(graph_theory).
- Zarankiewicz_problem wikiPageWikiLink Wacław_Sierpiński.
- Zarankiewicz_problem wikiPageWikiLink Štefan_Znám.
- Zarankiewicz_problem wikiPageWikiLink File:Zarankiewicz-4-3.svg.
- Zarankiewicz_problem wikiPageWikiLinkText "Kővári–Sós–Turán theorem".
- Zarankiewicz_problem wikiPageWikiLinkText "Zarankiewicz problem".
- Zarankiewicz_problem wikiPageWikiLinkText "Zarankiewicz problem#The K.C5.91v.C3.A1ri.E2.80.93S.C3.B3s.E2.80.93Tur.C3.A1n theorem".
- Zarankiewicz_problem wikiPageWikiLinkText "Zarankiewicz problem#The Kővári–Sós–Turán theorem".
- Zarankiewicz_problem wikiPageWikiLinkText "Zarankiewicz problem#The_K.C5.91v.C3.A1ri.E2.80.93S.C3.B3s.E2.80.93Tur.C3.A1n_theorem".
- Zarankiewicz_problem wikiPageWikiLinkText "Zarankiewicz problem#Upper bounds".
- Zarankiewicz_problem wikiPageUsesTemplate Template:Reflist.
- Zarankiewicz_problem subject Category:Extremal_graph_theory.
- Zarankiewicz_problem subject Category:Mathematical_problems.
- Zarankiewicz_problem subject Category:Unsolved_problems_in_mathematics.
- Zarankiewicz_problem type Redirect.
- Zarankiewicz_problem comment "The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices but has no complete bipartite subgraphs of a given size. It belongs to the field of extremal graph theory, a branch of combinatorics, and is named after the Polish mathematician Kazimierz Zarankiewicz, who proposed several special cases of the problem in 1951.The Kővári–Sós–Turán theorem, named after Tamás Kővári, Vera T.".
- Zarankiewicz_problem label "Zarankiewicz problem".
- Zarankiewicz_problem sameAs Q8066611.
- Zarankiewicz_problem sameAs m.09fs3_.
- Zarankiewicz_problem sameAs Q8066611.
- Zarankiewicz_problem wasDerivedFrom Zarankiewicz_problem?oldid=702194713.
- Zarankiewicz_problem depiction Zarankiewicz-4-3.svg.
- Zarankiewicz_problem isPrimaryTopicOf Zarankiewicz_problem.