Kazimierz Zarankiewicz

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Kazimierz Zarankiewicz (May 2, 1902 – September 5, 1959) was a Polish mathematician who worked mainly in topology and graph theory. He was born in Częstochowa, studied at the University of Warsaw, and later became a professor at the Warsaw University of Technology. During World War II he taught illegally under German occupation and was sent to a concentration camp; he survived and continued teaching after the war. He visited universities in Tomsk, Harvard, London and Vienna, and he served as president of the Warsaw section of the Polish Mathematical Society and of the International Astronautical Federation. He died in London, England.

Zarankiewicz is best known for problems and conjectures in combinatorics. The Zarankiewicz problem asks, for a given 0-1 matrix, how many 1s are needed to force a submatrix of all 1s of a given size; in graph terms, it asks for the maximum number of edges in a bipartite graph that does not contain a complete bipartite subgraph Km,n. The Zarankiewicz crossing number conjecture concerns the crossing number of complete bipartite graphs Km,n; Zarankiewicz showed that the proposed formula gives an upper bound for the actual crossing number. He also wrote on other topics in topology, complex analysis, and number theory, including triangular numbers.