György Hajós

György Hajós (around 1930)

György Hajós , Hungarian Hajós György , also cited by Georg Hajós , (* February 21, 1912 in Budapest ; † March 17, 1972 ibid.) Was a Hungarian mathematician who mainly dealt with geometry .

life and work

He studied at the Péter Pázmány University (later renamed Loránd Eötvös University ), where he graduated in 1929. As a student he gave a simple proof of a lattice geometry theorem by Hermann Minkowski . After graduation he was a teacher and from 1935 lecturer and private tutor at the Technical University of Budapest. He received his doctorate in 1938. From 1949 he was professor and head of the geometry department at the Loránd Eötvös University in Budapest.

Hajós was secretary of the Mathematical-Physical Section of the Hungarian Academy of Sciences. For many years he was president of the Mathematical Society Janós Bolyai and for 10 years editor of the Acta Mathematica Academiae Scientiarum Hungaricae

Among other things, he dealt with nomography , error calculation , non-Euclidean geometry , discrete geometry, elementary geometry .

In 1941 he proved that Hermann Minkowski had already suspected a tightening of his linear form theorem in the geometry of numbers, the Minkowski-Hajós theorem, on which many well-known mathematicians had previously failed. There was a transition from less than or equal to relations in the inequalities of the linear form theorem to strict small relations. For this he received the Gyula König Prize of the Mathematical and Physical Society Lorand Eötvös in 1942. Hajós had transformed the geometrical problem into a group theoretical one and proved it. The proof of the group-theoretical theorem was simplified by László Rédei and the theorem was generalized.

In 1948 he became a corresponding and in 1953 a full member of the Hungarian Academy of Sciences . He had been a member of the Leopoldina since 1967 and a corresponding member of the Romanian Academy of Sciences (1965). In 1951 and 1962 he received the Kossuth Prize and the Beke Manó Memorial Prize. He received the Order of the Lion of Finland .

The Hajós conjecture of graph theory and another unsolved conjecture (cycle conjecture by Hajos) about circular decomposition of Euler graphs from 1968 (every simple graph with n nodes that have even degrees can be decomposed into circles at most ) comes from him ). The general case is unsolved, but it was proved for small graphs ( ) 2017 and for path widths less than or equal to 6. ${\displaystyle {\frac {1}{2}}(n-1)}$ ${\displaystyle n\leq 12}$

Fonts

• Introduction to Geometry, Leipzig , Teubner Verlag , Akadémiai Kiadó , Budapest 1970, new edition Harri Deutsch 2001
• Editor with József Kürschák , Gyula Neukomm , János Surányi : Hungarian Problem Book, Part 1 (based on the Eötvös Competitions 1894-1905), Part 2 (based on the Eötvös Competitions 1906-1928) , MAA , Random House 1963
• Editor with Gyula Neukomm, János Surányi: Hungarian problem book III: based on the Eötvös Competitions, 1929–1943 , MAA 2001

See also

• Moser spindle (Hajos graph)
• Interval graph

Web links

• biography
• Hajós György in Magyar Életrajzi Lexicon ( Hungarian )

References

1. ↑ Hajós On a new representation of hyperbolic trigonometry using the Poincaré model , Annales Univ. Sci. Budapestiensis etc., Sectio Math., Vol. 7, 1964 (Hungarian)
2. ^ Like Oskar Perron , Nikolaus Hofreiter , Ott-Heinrich Keller
3. ↑ Hajós About single and multiple covering of the n-dimensional space with a cube grid , Mathematische Zeitschrift, Vol. 47, 1942, p. 427, Online  ( page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.  
4. ↑ Irene Heinrich, Marco Natale, Manuel Streicher, Hajós' cycle conjecture for small graphs , Arxiv 2017
5. ↑ Elke Fuchs, Laura Gellert, Irene Heinrich: Cycle decompositions of pathwidth-6 graphs , Arxiv 2017