Zarankiewicz proved that this formula is an upper bound for the actual crossing number. The problem of determining the number was suggested by Paul Turán and became known as Turán's brick factory problem.
kazimierz, zarankiewicz, 1902, september, 1959, polish, mathematician, professor, warsaw, university, technology, interested, primarily, topology, graph, theory, zarankiewicz, moscow, 1935born, 1902, 1902częstochowa, congress, poland, russian, empiredied5, sep. Kazimierz Zarankiewicz 2 May 1902 5 September 1959 was a Polish mathematician and Professor at the Warsaw University of Technology who was interested primarily in topology and graph theory Kazimierz ZarankiewiczZarankiewicz in Moscow 1935Born 1902 05 02 2 May 1902Czestochowa Congress Poland Russian EmpireDied5 September 1959 1959 09 05 aged 57 London EnglandNationalityPolishAlma materUniversity of WarsawKnown forZarankiewicz problemZarankiewicz crossing number conjectureScientific careerFieldsTopology Graph theoryInstitutionsUniversity of Warsaw Contents 1 Biography 2 Research contributions 3 See also 4 References 5 External linksBiography Edit Grave of Kazimierz Zarankiewicz in Powazki Cemetery WarsawZarankiewicz was born in Czestochowa to father Stanislaw and mother Jozefa nee Borowska 1 He studied at the University of Warsaw together with Zygmunt Janiszewski Stefan Mazurkiewicz Waclaw Sierpinski Kazimierz Kuratowski and Stanislaw Saks During World War II Zarankiewicz took part in illegal teaching forbidden by the German authorities and eventually was sent to a concentration camp He survived and became a teacher at Warsaw University of Technology Polish Politechnika Warszawska 2 He visited universities in Tomsk Harvard London and Vienna He served as president of the Warsaw section of the Polish Mathematical Society and the International Astronautical Federation He died in London England Research contributions EditZarankiewicz wrote works on cut points in connected spaces on conformal mappings on complex functions and number theory and triangular numbers The Zarankiewicz problem is named after Zarankiewicz This problem asks for a given size of 0 1 matrix how many matrix entries must be set equal to 1 in order to guarantee that the matrix contains at least one a b submatrix is made up only of 1 s An equivalent formulation in extremal graph theory asks for the maximum number of edges in a bipartite graph with no complete bipartite subgraph Ka b The Zarankiewicz crossing number conjecture in the mathematical field of graph theory is also named after Zarankiewicz The conjecture states that the crossing number of a complete bipartite graph K m n displaystyle K m n equals cr K m n n 2 n 1 2 m 2 m 1 2 displaystyle text cr K m n left lfloor frac n 2 right rfloor left lfloor frac n 1 2 right rfloor left lfloor frac m 2 right rfloor left lfloor frac m 1 2 right rfloor Zarankiewicz proved that this formula is an upper bound for the actual crossing number The problem of determining the number c r K m n displaystyle cr K m n was suggested by Paul Turan and became known as Turan s brick factory problem See also EditList of Polish mathematiciansReferences Edit Wieslaw Wojcik Zarankiewicz Kazimierz Jozef gigancinauki pl in Polish Retrieved 2 February 2023 Kazimierz Zarankiewicz Retrieved 2 February 2023 External links Edit Wikimedia Commons has media related to Kazimierz Zarankiewicz mathematician O Connor John J Robertson Edmund F Kazimierz Zarankiewicz MacTutor History of Mathematics Archive University of St Andrews Retrieved from https en wikipedia org w index php title Kazimierz Zarankiewicz amp oldid 1137235175, wikipedia, wiki, book, books, library,
