Heiko Harborth

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

Life

Harborth went to high school in Bad Iburg and Wolfenbüttel (Abitur in 1958) and studied mathematics and physics at the Technical University of Braunschweig from 1958 to 1964 with the aim of becoming a high school teacher. In 1964 he became an assistant in Braunschweig and in 1965 he received his doctorate there under Hans-Joachim Kanold . In 1972 he completed his habilitation in Braunschweig, where he became associate professor in 1975 and professor in 1978.

In 2007 he received the Euler Medal with Stephen Milne . He is a member of the Braunschweigische Wissenschaftliche Gesellschaft , the New York Academy of Sciences and the Institute of Combinatorics and its Applications.

From 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 of Geombinatorics .

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

Harborth graph

plant

The eponymous Harborth graph (1986) is the smallest known example of a matchstick graph (Matchstick graph), in which each node exactly four neighbors (he is 4-regular ). As the name suggests, match graphs can be modeled with matches of the same length on a flat surface (that is, the edges are of unit length and the graph is planar). The Harborth conjecture says that every planar graph has a straight line embedding in the plane, in which the straight line segments corresponding to the edges have integer values. It has long been known that every planar graph has a straight-line embedding in the plane (theorem of Fáry , 1948). The conjecture has been proven for cubic graphs (every node has exactly three neighbors), the general case is open.

He proved a theorem of the Happy Ending Theorem type by 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 with ten or more points in general position in plane five of these points define a convex pentagon that does not contain any of the other points.

In 1974 he solved the coin graph problem in discrete geometry, which asks for the maximum number of edges in a coin graph (so called because it is created from spherical packings) with n nodes and uniform edge length (the disks all have the same radius). Harborth found for the maximum number of edges .

The Stolarsky-Harborth constant is named after him and Kenneth Stolarsky.

He also dealt with the history of mathematics (with Richard Dedekind, among others ).

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ^ The ICA Medals. Institute of Combinatorics and its Applications, accessed June 15, 2018 .
  3. ↑ Harborth: Match Sticks in the Plane. In: Richard K. Guy , RE Woodrow (Ed.): The Lighter Side of Mathematics. Proceedings of the Eugéne Strens Memorial Conference of Recreational Mathematics & its History. Calgary, Canada, July 27-August 2, 1986; Washington, DC: Mathematical Association of America , 1994, pp. 281-288.
  4. ↑ Harborth, A. Kemnitz, M. Möller, A. Süssenbach: Integer planar representations of the platonic solids. Elements of Mathematics, Volume 42, 1987, pp. 118-122; Harborth, A. Kemnitz: Plane integral drawings of planar graphs. Discrete Math., Vol. 236, 2001, pp. 191-195.
  5. ↑ Also proven independently of Klaus Wagner in 1936
  6. ↑ Jim Geelen, Anjie Guo, David McKinnon: Straight Line Embedding of cubic planar graphs with integer edge lengths. J. of Graph Theory, Volume 58, 2008, pp. 270-274, Online, PDF.
  7. ↑ Harborth: Convex pentagons in flat sets of points. Elements of Mathematics, Volume 33, 1978, pp. 116-118.
  8. ↑ The nodes correspond to the centers of the spheres or discs, whereby the spheres do not overlap. Two nodes are connected when the corresponding spheres touch.
  9. ↑ Harborth: Solution to Problem 664A. Elements of Mathematics, Volume 29, 1974, pp. 14-15. The problem goes back to Erdős in 1946.
  10. ^ Stolarsky-Harborth constant at Mathworld
  11. ↑ Harborth: Number of Odd Binomial Coefficients. Proc. Amer. Math. Soc. Volume 62, 1977, pp. 19-22.
personal data
SURNAME Harborth, Heiko
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH February 11, 1938
PLACE OF BIRTH Celle