Professor Gerhard Ringel

Professor Gerhard Ringel

Tuesday, November 9, 2010

Pioneer of Graph Theory

Gerhard Ringel in collaboration with J.W.T. Youngs is accredited with the solution of the Heawood conjecture. They proved Heawood's assumption that you need only four colors to create a political map on any surface in such a way that each country is colored differently then its adjacent countries. An article called: "Solution of the Heawood map-coloring problem" published in 1968 represents the result of their research. The former Heawood conjecture could now be named Ringel-Youngs Theorem: H(p) = [ 1/2( 7 + √( 48p + 1)) ]. Ringel's proof marks a turning point in topology because it was developed before the digital revolution and relies on the capacity of the human brain itself. In 1976 the mathematicians Appel and Haken used a computer to prove the Four Color Theorem which is a case of the Heawood conjecture.

Along with Erdös, Harary and others Ringel was a trailblazer who revived and developed the discipline of graph theory in the early fifties of the 20th century. A number of his conjectures, among them the Ringel's conjecture, the Ringel-Kotzig conjecture, the Oberwolfach problem and the Earth Moon problem, are part of his legacy and inspire the next generation of graph theorists to continue his work.

Ringel published about eighty articles and three books: "Färbungsprobleme auf Flächen und Graphen"(Berlin 1963), "Map Color Theorem"(Berlin 1970 with a new edition in 2011) and a popular textbook "Pearls in Graph Theory" with co author Nora Hartsfield (London 1990 with a new edition in 2003). Besides numerous well illustrated exercises it contains a comprehensive introduction to graph theory of outstanding scholarly depth and clarity. "Map Color Theorem" was translated into Russian in 1974 and "Pearls in Graph Theory" was translated into Japanese in 2012.

Besides publishing Ringel transmitted the results of his research through his charismatic lectures. The sparkle in his blue eyes while he presented a particularily convincing solution became legendary. Unlike many other scientists he couldn’t care less about increasing the list of his publications. Teaching was his focus. He loved to share the joy of mathematical discovery with both experts and beginners. Professor Ringel did not have a desk in his house. He spent many hours filling an endless amount of writing pads with drawings and notes while comfortably curled up on his sofa. In his younger years he used to be so absorbed in his research that he did not see or hear anybody or anything around him.

Ringel has an Erdos number of 2 because of his collaboration with R. Guy from Calgary. Some of his mathematical findings were fundamental for economic theories and earned him in 1983 a honorary doctorate in political science from the Universität Karlsruhe. He received a second honorary doctorate in mathematics from the Freie Universität Berlin in 1994. On his 70th birthday he was honored by a collection of essays in the book: “Topics in Combinatorics and Graph Theory” edited by R. Bodendiek. L.W. Beineke and R. Wilson dedicated their 2009 book: “Topics in Topological Graphtheory” to his memory.

Gerhard Ringel was born 10/28/1919 in Kollnbrunn, Austria. He studied mathematics at the Charles University in Prague and after World War II at the Friedrich-Wilhelms- Universität in Bonn where he received his PhD in 1951. He became professor in 1958 and started teaching at the Freie Universität Berlin where he was chairman of the mathematical institute from 1967 until 1970. He started his career at UCSC in 1968 as visiting Professor and became a full professor in 1970. He was chairman of the math department for twelve years (1972 - 1984). His laissez faire style authority and calm friendly presence are fondly remembered by his students, colleagues and staff. He died June 24th 2008 in Santa Cruz.


  1. I was saddened to read about his passing. I took his graph theory class at UCSC in the early 1990s. All of the other people in the class called him Gerhard, but for some reason I had to address him as Herr Doktor Ringel. I guess that was because of all the years I spent in Germany and being married to a German. To this day, I remember his class with great fondness and am honored to have had him as my teacher.

  2. He was one of my professors back in Berlin 1966/1967 in my first university year. I remember 2 incidents.

    He had to read about analysis for about 200 freshmen. The course began at 8:15 in the morning and ended at 10:00.

    Someone must have complained about the early hour, because he told us that an early beginning has the invaluable advantage of early after-hours. We would be free even before noon.

    After a while, someone else complained about the exercises. Most of us, including myself, didn't have a faint idea of how to deal with them. He answered with his theory about creativity.

    We should not worry but rather let go for the day if we had no idea. At night, during sleep, our brain would work on these problems and in the morning, we should have another look. In due time, we would be able to develop a solution. After all, deadline would be in a week.

    Years later I learned that this theory had been proposed at the end of the 19th century by Poincaré based on his own, quite drastic experiences.

    1. Thanks for your comment and interesting observation!