Camillo Herbert Grötzsch (21 May 1902 – 15 May 1993) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He was born in

Döbeln Döbeln ( hsb, Doblin) is a town in Saxony, Germany, part of the Mittelsachsen district, on both banks of the river Freiberger Mulde. History * 981: First written mention of Döbeln (Margravate of Meissen). * Around 1220: Döbeln is described ...

and died in

Halle Halle may refer to: Places Germany * Halle (Saale), also called Halle an der Saale, a city in Saxony-Anhalt ** Halle (region), a former administrative region in Saxony-Anhalt ** Bezirk Halle, a former administrative division of East Germany ** Hall ...

. Grötzsch worked in

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

. He was the discoverer and eponym of the Grötzsch graph, a triangle-free graph that requires four colors in any

graph coloring In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices o ...

, and Grötzsch's theorem, the result that every triangle-free

planar graph In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross ...

requires at most three colors. A student of Paul Koebe, he made important contributions to the theory of conformal mappings and

univalent function In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective. Examples The function f \colon z \mapsto 2z + z^2 is univalent in the open unit disc, as f(z ...

s: he was the first to introduce the concept of a

quasiconformal mapping In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let ''f'' : ''D' ...

Publications

*Herbert Grötzsch, Über die Verzerrung bei schlichten nicht-konformen Abbildungen und über eine damit zusammenhängende Erweiterung des Picardschen Satzes, Sitzungsberichte sächs. Akad. Wiss., Math.-Phys. Klasse, vol. 80, 1928, pp. 503–507

References

* * * Reiner Kühnau, ''Herbert Grötzsch zum Gedächtnis''. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 99, 1997, pp. 122–145 (1997) * Reiner Kühnau, ''Einige neuere Entwicklungen bei quasikonformen Abbildungen''. Jahresbericht Deutscher Mathematikervereinigung, vol. 94, pp. 141–192 (1992) * Horst Tietz, ''Herbert Grötzsch in Marburg''. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 99, 1997, pp. 146–148

External links

Oberwolfach Photo Collection
{{DEFAULTSORT:Grotzsch, Herbert 1902 births 1993 deaths 20th-century German mathematicians Graph theorists Complex analysts People from Halle (Saale)