Carl Hierholzer

Carl Hierholzer (1840-September 13 1871) was a German mathematician.

Hierholzer studied mathematics in Karlsruhe, and he got his PhD from Ruprecht-Karls-Universität Heidelberg in 1865. His PhD advisor was Ludwig Otto Hesse (1811–1874). In 1870 Hierholzer wrote his habilitation about conic sections (title: "Ueber Kegelschnitte im Raum") in Karlsruhe, where he later became professor.

Hierholzer proved that a graph has an Eulerian cycle if and only if it is connected and every vertex has an even degree. This result had been given, without proof, by Leonard Euler in 1736. Hierholzer apparently explained his proof, just before his premature death in 1871, to a colleague who then arranged for its posthumous publication which appeared in 1873 (title: "Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren".)

References

* C. Hierholzer: "Ueber Kegelschnitte im Raume". (Habilitation in Karlsruhe.) Mathematische Annalen II (1870), 564–586. [http://jfm.sub.uni-goettingen.de/JFM/digit.php?an=JFM+02.0570.02] [http://www.springerlink.com/content/w467754q536h0167/]
* C. Hierholzer: "Ueber eine Fläche der vierten Ordnung". Mathematische Annalen IV (1871), 172–180. [http://gdz.sub.uni-goettingen.de/index.php?id=img&no_cache=1&IDDOC=26054] [http://www.springerlink.com/content/r564251217377210/]
* C. Hierholzer: "Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren". Mathematische Annalen VI (1873), 30–32. [http://jfm.sub.uni-goettingen.de/JFM/digit.php?an=JFM+05.0286.02] [http://www.springerlink.com/content/x4458623778t4704/]
* Barnett, J.H., "Early Writings on Graph Theory: Euler Circuits and The Königsberg Bridge Problem" [http://www.math.nmsu.edu/hist_projects/Euler-Barnett.pdf]