Rudolf Halin

Rudolf Halin (February 3, 1934 – November 14, 2014) was a German graph theorist, known for defining the ends of infinite graphs,^[1] for Halin's grid theorem,^[2][3] for extending Menger's theorem to infinite graphs,^[4] and for his early research on treewidth and tree decomposition.^[5] He is also the namesake of Halin graphs, a class of planar graphs constructed from trees by adding a cycle through the leaves of the given tree; earlier researchers had studied the subclass of cubic Halin graphs but Halin was the first to study this class of graphs in full generality.^[6]

Life

Halin was born on February 3, 1934, in Uerdingen.^[7] He earned his doctorate from the University of Cologne in 1962, under the supervision of Klaus Wagner and Karl Dörge, after which he joined the faculty of the University of Hamburg.^[8] He died on November 14, 2014, in Mölln, Schleswig-Holstein.^[7]

Recognition

In February 1994, a colloquium was held at the University of Hamburg in honor of Halin's 60th birthday.^[9] In 2017, a special issue of the journal Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg was published in his memory.^[10]

Selected publications

Research papers

• Halin, R. (1964), "Über unendliche Wege in Graphen", Mathematische Annalen, 157 (2): 125–137, doi:10.1007/bf01362670, hdl:10338.dmlcz/102294, MR 0170340, S2CID 122125458.
• Halin, R. (1965), "Über die Maximalzahl fremder unendlicher Wege in Graphen", Mathematische Nachrichten, 30 (1–2): 63–85, doi:10.1002/mana.19650300106, MR 0190031.
• Halin, R. (1971), "Studies on minimally n-connected graphs", Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), London: Academic Press, pp. 129–136, MR 0278980.
• Halin, R. (1974), "A note on Menger's theorem for infinite locally finite graphs", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 40: 111–114, doi:10.1007/BF02993589, MR 0335355, S2CID 120915644.
• Halin, R. (1976), "S-functions for graphs", Journal of Geometry, 8 (1–2): 171–186, doi:10.1007/BF01917434, MR 0444522, S2CID 120256194.

Textbooks

• Halin, R., Graphentheorie. Vols. I and II published in 1980 and 1981 respectively by Wissenschaftliche Buchgesellschaft.^[11] Combined 2nd ed. published in 1989 by Wissenschaftliche Buchgesellschaft.^[12]

References

1. Halin (1964).
2. Halin (1965).
3. Diestel, Reinhard (2004), "A short proof of Halin's grid theorem", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 74: 237–242, doi:10.1007/BF02941538, MR 2112834, S2CID 124603912.
4. Halin (1974).
5. Halin (1976).
6. Halin (1971).
7. Diestel, Reinhard (December 7, 2014), Rudolf Halin 1934–2014, DMANET mailing list. Date corrected in a follow-up email from Diestel. Birthplace from his books Graphentheorie I, II.
8. Rudolf Halin at the Mathematics Genealogy Project
9. Mathematisches Seminar, Univ. of Hamburg, retrieved 2013-02-19.
10. Diestel, Reinhard (2017), "Rudolf Halin: 1934–2014", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 87 (2): 197–202, doi:10.1007/s12188-016-0161-2, MR 3696145
11. Vol. I, ISBN 3-534-06767-3. Reviewed by W. Dörfler, MR0586234. Vol. II, ISBN 3-534-06767-3. Reviewed by W. Dörfler, MR0668698.
12. ISBN 3-534-10140-5. MR1068314.