Graph minor theory | Planar graphs | Theorems in graph theory

Wagner's theorem

In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite graph is planar if and only if its minors include neither K5 (the complete graph on five vertices) nor K3,3 (the utility graph, a complete bipartite graph on six vertices). This was one of the earliest results in the theory of graph minors and can be seen as a forerunner of the Robertson–Seymour theorem. (Wikipedia).

Wagner's theorem
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Related pages

Kelmans–Seymour conjecture | K-vertex-connected graph | Graph (discrete mathematics) | Planar graph | Wagner graph | Graphic matroid | Klaus Wagner | Multigraph | Path (graph theory) | Graph structure theorem | Matroid | Graph theory | Graph minor | Complete bipartite graph | Vertex (graph theory) | Complete graph | Euclidean plane | Kuratowski's theorem | Forbidden graph characterization | Utility graph | Matroid minor | Graph embedding | Clique-sum | Robertson–Seymour theorem