Rudolf Halin (February 3, 1934 – November 14, 2014) was a German graph theorist, known for defining the

ends End, END, Ending, or variation, may refer to: End *In mathematics: **End (category theory) **End (topology) **End (graph theory) ** End (group theory) (a subcase of the previous) **End (endomorphism) *In sports and games **End (gridiron football) ...

of infinite graphs, for

Halin's grid theorem In graph theory, a branch of mathematics, Halin's grid theorem states that the infinite graphs with thick ends are exactly the graphs containing subdivisions of the hexagonal tiling of the plane. It was published by , and is a precursor to the wo ...

, for extending Menger's theorem to infinite graphs, and for his early research on treewidth and

tree decomposition In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees ...

. He is also the namesake of

Halin graph In graph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle. The tree must have at least four vertices, none of which has exactly two neighbors; it should be drawn in the plane so none of ...

s, a class of

planar graph In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross ...

s constructed from trees by adding a cycle through the leaves of the given tree; earlier researchers had studied the subclass of

cubic Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system w ...

Halin graphs but Halin was the first to study this class of graphs in full generality.

Life

Halin was born on February 3, 1934 in Uerdingen.. Date corrected in a follow-up email from Diestel. Birthplace from his books ''Graphentheorie I, II''. He earned his doctorate from the University of Cologne in 1962, under the supervision of

Klaus Wagner Klaus Wagner (March 31, 1910 – February 6, 2000) was a German mathematician known for his contributions to graph theory. Education and career Wagner studied topology at the University of Cologne under the supervision of who had been a student ...

and Karl Dörge, after which he joined the faculty of the University of Hamburg. He died on November 14, 2014, in

Mölln, Schleswig-Holstein Mölln () is a town in Schleswig-Holstein, Germany. It is surrounded by several small lakes (Stadtsee, Schulsee, Ziegelsee, Hegesee, Schmalsee, Lütauer See, Drüsensee, and Pinnsee). The Elbe-Lübeck Canal flows through the town. Mölln bel ...

Recognition

In February 1994, a colloquium was held at the University of Hamburg in honor of Halin's 60th birthday. In 2017, a special issue of the journal ''Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg'' was published in his memory.

Selected publications

Research papers

*. *. *. *. *.

Textbooks

*Halin, R., ''Graphentheorie''. Vols. I and II published in 1980 and 1981 respectively by Wissenschaftliche Buchgesellschaft. Combined 2nd ed. published in 1989 by Wissenschaftliche Buchgesellschaft.. .

References

{{DEFAULTSORT:Halin, Rudolf 1934 births 2014 deaths 20th-century German mathematicians Graph theorists University of Cologne alumni Academic staff of the University of Hamburg