Gerhard Ringel

Gerhard Ringel while surfing

Gerhard Ringel (born October 28, 1919 in Kollnbrunn ; † June 24, 2008 in Santa Cruz ) was a German mathematician and pioneer in the field of combinatorics and graph theory .

Live and act

Ringel grew up in Bohemia (in addition to German he also spoke fluent Czech), graduated from high school in Braunau and began studying mathematics at the Charles University in Prague . From 1940 he was drafted into military service in World War II and was a Soviet prisoner of war for four and a half years (since then he has spoken fluent Russian). After his return he studied mathematics at the University of Bonn from 1949 , where he received his doctorate in 1951 under Emanuel Sperner ( color set for non-orientable surfaces of any gender ).

After his habilitation in 1953, he was a lecturer at the University of Bonn , where he taught from 1956. From 1957 to 1960 he taught at the Johann Wolfgang Goethe University in Frankfurt am Main , and from 1958 as a professor. From 1960 he was a professor at the Free University of Berlin (with a full professorship from 1966). From 1967 to 1970 he was head of the Mathematical Institute there. In 1969 he went to the University of California, Santa Cruz (UCSC) as an Associate Professor at the Free University of Berlin (student unrest ), where he was visiting professor as early as 1968. In 1970 he was given a full professorship there and was director of the second mathematical institute. From 1972 to 1984 he was head of the mathematics faculty. From 1990 he was Professor Emeritus. At the University of Santa Cruz he was known as an outstanding teacher.

He published around 80 scientific articles and three books. His research was honored with honorary doctorates from the University of Karlsruhe (1983 in Political Science) and the Free University of Berlin (1994).

In collaboration with JWT Youngs , he proved the Heawood Conjecture in 1968 (after Percy Heawood ), the generalization of the four-color theorem for surfaces of any gender , but not for gender zero, the case of the plane or sphere from which the four- Colors set deals. The Heawood conjecture has since been called the Ringel Youngs theorem .

More precisely, they proved that the minimum number of colors required by gender to color any map on an orientable surface , also called the chromatic number of the surface, is given by the formula ${\displaystyle S_{p}}$ ${\displaystyle p>0}$ ${\displaystyle \chi (S_{p})}$

${\displaystyle \chi (S_{p})={\biggl \lfloor }{\frac {7+{\sqrt {1+48p}}}{2}}{\biggr \rfloor }}$

given is. Heawood had already proven in 1890 that the chromatic number is less than or equal to the number on the right-hand side. In 1891 Lothar Heffter pointed out that his proof did not also prove equality . Heawood proved this only for the case , the case of the torus , and Heffter proved a few more cases. In his dissertation, Ringel proved the inequality for non-orientable surfaces. ${\displaystyle p=1}$

He is also known for some problems in graph theory ( Oberwolfach problem , Ringel-Kotzig conjecture with Anton Kotzig , earth-moon problem ).

In addition to his mathematical career, Ringel was also a well-known and valued entomologist and butterfly collector, who pursued his hobby in Africa, South America, Bali, Jamaica and New Zealand and bequeathed his extensive butterfly collection to the UCSC Museum during his lifetime.

In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( self-complementary graphs ).

literature

• Rainer Bodendiek, Rudolf Henn (Editor) Topics in Combinatorics and Graph Theory , Physica Verlag 1998 (Festschrift for the 70th birthday with biography)

Fonts

• with Nora Hartsfield: Pearls in graph theory . Academic Press, Boston, MA. 1990, 2003, ISBN 0-12-328552-6 .
• Coloring problems on surfaces and graphs . VEB Verlag der Wissenschaften, Berlin, 1959.
• Map Color Theorem . Springer-Verlag, New York / Berlin, 1974 (also translated into Russian)
• with JWT Youngs: Solution of the Heawood Map-Coloring Problem. (PDF file; 676 kB) . In: Proc. Nat. Acad. Sci. USA 60: 438-445, 1968.
• Ringel: Set of colors for non-orientable surfaces of any gender. Journal for Pure and Applied Mathematics, Vol. 190, 1952.
• Ringel: Set of colors for orientable areas of the sexes . ${\displaystyle p>0}$Journal for Pure and Applied Mathematics, Vol. 193, 1954.
• Card coloring problems. In: Konrad Jacobs : Selecta Mathematica. Vol. 3, Springer-Verlag.

Web links

• Literature by and about Gerhard Ringel in the catalog of the German National Library

• FREIE UNIVERSITÄT BERLIN 1948-1973 - University in transition
• Gerhard Ringel, professor emeritus of mathematics, dies at age 88. (English).
• English biography of his daughter
• Retired mathematics professor Gerhard Ringel gives his world-class butterfly collection to UCSC. (English; PDF file; 476 kB)
• Der Tagesspiegel, obituary Gerhard Ringel

Individual evidence

1. ↑ English-language curriculum vitae in American Men and Women of Science , Thomson Gale 2004, there Assistant Professor in Bonn from 1956. Probably private lecturer is meant.
2. ↑ biography on his daughter's website
3. ↑ Butterfly collection by Ringel, pdf ( Memento of the original from March 5, 2012 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.