Kuratowski’s theorem

A finite graph is planar if and only if it contains no subgraphMathworldPlanetmath that is isomorphicPlanetmathPlanetmath to or is a subdivision of K5 or K3,3, where K5 is the complete graphMathworldPlanetmath of order 5 and K3,3 is the complete bipartite graphMathworldPlanetmath with 3 vertices in each of the halfs. Wagner’s theorem is an equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath later result.


  • 1 Kazimierz Kuratowski. Sur le problème des courbes gauches en topologie. Fund. Math., 15:271–283, 1930.
Title Kuratowski’s theorem
Canonical name KuratowskisTheorem
Date of creation 2013-03-22 11:57:45
Last modified on 2013-03-22 11:57:45
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 12
Author bbukh (348)
Entry type Theorem
Classification msc 05C10
Related topic PlanarGraph
Related topic WagnersTheorem