In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite...

the Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Coleman theorem) states that continuous...

proof, the statement of the theorem was known as Wagner's conjecture after the German mathematician Klaus Wagner, although Wagner said he never conjectured...

— • — • ) zero or more times. Instead of considering subdivisions, Wagner's theorem deals with minors: A finite graph is planar if and only if it does...

this usage has not spread to other places. A closely related result, Wagner's theorem, characterizes the planar graphs by their minors in terms of the same...

can be formed from a larger graph by contracting and removing edges. Wagner's theorem characterizes the planar graphs as exactly those graphs that do not...

vertices and by contracting edges. The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the...

bicommutant theorem (functional analysis) Von Neumann's theorem (operator theory) Von Staudt–Clausen theorem (number theory) Wagner's theorem (graph theory)...

the drawing. Outerplanar graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two forbidden minors K4 and K2,3, or by their...

contains either K3,3 or the complete graph K5 as a minor; this is Wagner's theorem. Every complete bipartite graph. Kn,n is a Moore graph and a (n,4)-cage...