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Kazimierz Kuratowski announced at a meeting of the Warsaw Section of the Polish Mathematical Society that a graph is planar if and only if it does not contain a subgraph homeomorphic to either K-5, the complete graph on 5 vertices, or K-3-3, the complete bipartite graph on a bipartite set of (3, 3) vertices.

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Kazimierz Kuratowski
Planar Graphs and Kuratowski's Theorem
Friday, June 21, 1929