Klaus Wagner (March 31, 1910 – February 6, 2000) was a German mathematician known for his contributions to graph theory.

Wagner studied topology at the University of Cologne under the supervision of Karl Dörge [de] who had been a student of Issai Schur.

Another result of his, also known as Wagner's theorem, is that a four-connected graph is planar if and only if it has no K5 minor.

This characterization was used by Wagner to show that the case k = 5 of the Hadwiger conjecture on the chromatic number of Kk-minor-free graphs is equivalent to the four color theorem.

Neil Robertson and Paul Seymour finally published a proof of Wagner's conjecture in 2004 and it is now known as the Robertson–Seymour theorem.