Heiko Harborth

Heiko Harborth ( born February 11, 1938 in Celle ) is a German mathematician and university teacher who deals primarily with graph theory, combinatorics, discrete geometry and number theory.

Life

Harborth went in Bad Iburg and Wolfenbüttel, the Gymnasium ( High School 1958) and studied to become a high school teacher with the goal of 1958-1964 mathematics and physics at the TU Braunschweig. In 1964 he became an assistant in Brunswick and in 1965 he became a PhD with Hans -Joachim Kanold. In 1972 he habilitated in Braunschweig, in 1975 he became associate professor in 1978 and professor.

In 2007 he was awarded the Euler Medal with Stephen Milne. He is a member of the Brunswick Scientific Society, the New York Academy of Sciences and the Institute of Combinatorics and its Applications.

1988 to 2001 he was editor of the Mathematical semester reports and he was co-editor of the Fibonacci Quarterly, of Integers: Electronic Journal of Combinatorial Theory and Geocombinatorics.

1961 until her death in 1980, he was married to Karin Reisener, with whom he has two children, and since 1985 with Bärbel Peter.

Work

The Harborth graph named after him (1986 ) is the smallest example of a matchstick graph ( Matchstick graph) in which each node has exactly four neighbors (he is 4 -regular ). As the name implies are matchstick graph by the laying of matches each of the same length in the plane constructible ( that is, the edges have unit length and the graph is planar ). The Harborth conjecture states that every planar graph has a straight-line embedding into the plane, in which the edges have the corresponding line segments integer values. That every planar graph has a straight line embedding (Straight Line Embedding) in the plane, was known for some time ( set of Fary, 1948. ). The presumption is for cubic graphs ( each node has exactly three neighbors) proved the general case is open.

He proved a theorem on the type of Happy Ending theorem of Paul Erdős, George Szekeres and Esther Klein. While there, four points define a convex quadrilateral with five points in general position in the plane, Harborth proved that in ten or more points in general position in the plane of these five points determine a convex pentagon that contains none of the other points.

In 1974, he solved the Coin graph problem in discrete geometry, that after the maximum number of edges in a Münzgraph (so called because it arises from sphere packings ) with n vertices and uniform edge length requested ( the discs have all the same radius). Harborth found for the maximum number of edges.

According to him and Kenneth Stolarsky the Stolarsky - Harborth constant is named.

He also dealt with the history of mathematics (including Richard Dedekind ).