Klaus Wagner

Klaus Wagner (March 31, 1910 – February 6, 2000) was a German mathematician. He studied topology at the University of Cologne under the supervision of Karl Dörge,^(de) who had been a student of Issai Schur. Wagner received his Ph.D. in 1937, and taught at Cologne for many years himself. In 1970, he moved to the University of Duisburg, where he remained until his retirement in 1978.

Wagner was honored in 1990 by a festschrift on graph theory, and in June 2000, following Wagner's death, the University of Cologne hosted a Festkolloquium in his memory.

Graph minors

Wagner is known for his contributions to graph theory and particularly the theory of graph minors, graphs that 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 have as a minor either a complete graph K₅ on five vertices or a complete bipartite graph K_3,3 with three vertices on each side of its bipartition. That is, these two graphs are the only minor-minimal non-planar graphs. It is closely related to, but should be distinguished from, Kuratowski's theorem, which states that the planar graphs are exactly those graphs that do not contain as a subgraph a subdivision of K₅ or K_3,3.

Klaus Wagner (equestrian)

Klaus Wagner (16 January 1922 – 16 August 2001) was a German equestrian. He competed in equestrian at the 1952 Summer Olympics in Helsinki, where he won a silver medal in the team eventing, and placed fifth in the individual contest. He competed in equestrian at the 1956 Summer Olympics in Stockholm, where he won a silver medal in the team competition in eventing (along with August Lütke-Westhues and Otto Rothe).

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