Heiko Harborth (born 11 February 1938, in

Celle Celle () is a town and capital of the district of Celle, in Lower Saxony, Germany. The town is situated on the banks of the river Aller, a tributary of the Weser, and has a population of about 71,000. Celle is the southern gateway to the Lü ...

, Germany)Harborth's web site http://www.mathematik.tu-bs.de/harborth/ . Accessed 14 May 2009. is Professor of

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

at Braunschweig University of Technology, 1975–present, and author of more than 188 mathematical publications.AMS MathSciNet http://www.ams.org/mathscinet . Accessed 14 May 2009. His work is mostly in the areas of number theory,

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

and discrete geometry, including graph theory.

Career

Harborth has been an instructor or professor at Braunschweig University of Technology since studying there and receiving his PhD in 1965 under Hans-Joachim Kanold. Harborth is a member of the New York Academy of Sciences, Braunschweigische Wissenschaftliche Gesellschaft, the Institute of Combinatorics and its Applications, and many other mathematical societies. Harborth currently sits on the editorial boards of Fibonacci Quarterly, Geombinatorics, Integers: Electronic Journal of Combinatorial Number Theory. He served as an editor of Mathematische Semesterberichte from 1988 to 2001. Harborth was a joint recipient (with

Stephen Milne Stephen Milne (born 8 March 1980) is a former professional Australian rules footballer who played for the St Kilda Football Club in the Australian Football League (AFL). A small forward, he held the record for the most games played by a play ...

) of the 2007 Euler Medal.

Mathematical work

Harborth's research ranges across the subject areas of

, graph theory, discrete geometry, and number theory. In 1974, Harborth solved the unit coin graph problem,Heiko Harborth, Lösung zu Problem 664A, Elem. Math. 29 (1974), 14–15. determining the maximum number of edges possible in a unit coin graph on n vertices. In 1986, Harborth presented the graph that would bear his name, the Harborth graph. It is the smallest known example of a 4- regular matchstick graph. It has 104 edges and 52 vertices. In connection with the

happy ending problem In mathematics, the "happy ending problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement: This was one of the original results that led to the development of Ramsey t ...

, Harborth showed that, for every finite set of ten or more points in general position in the plane, some five of them form a convex pentagon that does not contain any of the other points. Harborth's conjecture posits that every planar graph admits a straight-line embedding in the plane where every edge has integer length. This open question () is a stronger version of Fáry's theorem. It is known to be true for cubic graphs. In number theory, the Stolarsky–Harborth constant is named for Harborth, along with Kenneth Stolarsky.

Private life

Harborth married Karin Reisener in 1961, and they had two children. He was widowed in 1980. In 1985 he married Bärbel Peter and with her has three stepchildren.

Notes

{{DEFAULTSORT:Harborth, Heiko 1938 births Living people Combinatorialists 20th-century German mathematicians 21st-century German mathematicians People from Celle Academic staff of the Technical University of Braunschweig