Wagner's theorem
= Wagner's theorem
{wiki=Wagner's_theorem}
Wagner's theorem is a result in graph theory that provides a characterization of planar graphs. Specifically, it states that a graph is planar if and only if it does not contain a subgraph that is a subdivision of the complete graph \\( K_\{5\} \\) (the complete graph on five vertices) or a subdivision of the complete bipartite graph \\( K_\{3,3\} \\) (the complete bipartite graph with three vertices in each part).