Star of David theorem: Difference between revisions

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{{Infobox scientist
|name              = Jenő Egerváry
|image            = Jenő_Egerváry.jpg
|image_size        = 150px
|birth_date        = {{birth date|1891|4|16}}
|birth_place      = [[Debrecen]], [[Kingdom of Hungary|Hungary]]
|death_date        = {{death date|1958|11|30}}
|death_place      = [[Budapest]], [[People's Republic of Hungary|Hungary]]
|nationality      = [[Hungary|Hungarian]]
|fields            = [[Mathematician]]
|alma_mater        = [[Eötvös Loránd University|University of Pázmány Péter]]
|doctoral_advisor  = [[Lipót Fejér|Leopold Fejér]]
|known_for        = [[König–Egerváry theorem]]
|awards            = [[Gyula König Prize]] (1932), [[Kossuth Prize]] (1949)
}}
'''Jenő Egerváry''' (or '''Eugene Egerváry''') (April 16, 1891 – November 30, 1958) was a [[Hungary|Hungarian]] [[mathematician]].


==Biography==
Egerváry was born in [[Debrecen]] in 1891. In 1914, he received his doctorate at the [[Eötvös Loránd University|Pázmány Péter University]] in Budapest, where he studied under the supervision of [[Lipót Fejér]]. He then worked as an assistant at the Seismological Observatory in Budapest, and since 1918 as a professor at the Superior Industrial School in Budapest. In 1938 he was appointed [[Privatdozent]] at the Pázmány Péter University in Budapest.{{sfn|Rózsa|1984}}


In 1941 he became full professor at the [[Technical University of Budapest]], and in 1950 he was  appointed Chairman of the Scientific Council of the [[Alfréd Rényi Institute of Mathematics|Research Institute for Applied Mathematics]] of the [[Hungarian Academy of Sciences]].{{sfn|Horváth|2005}}
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Egerváry received the [[Gyula König]] Prize in 1932 and the [[Kossuth Prize]] in 1949.{{sfn|Horváth|2005}}
 
He committed suicide in 1958 because of the troubles caused to him by the communist bureaucracy.<ref name='Spedicato'>{{cite journal|title=Ricordo di Egerváry|journal=Notiziario dell'Unione Matematica Italiana|date=November 2008|year=2008|first=Emilio|last=Spedicato|coauthors=|language=Italian|volume=|issue=|pages=|id= |url=http://umi.dm.unibo.it/old/italiano/Editoria/NUMI2008/novembre08.pdf
|format= }}</ref>
 
==Works==
Egerváry's interests spanned the [[theory of equations|theory of algebraic equations]], [[geometry]], [[differential equation]]s, and [[Matrix (mathematics)|matrix theory]].{{sfn|Rózsa|1984}}
 
In what later became a classic result in the field of [[combinatorial optimization]],<ref name='Schrijver'>{{cite book | last = Schrijver | first = Alexander | authorlink = Alexander Schrijver | coauthors = | title = Combinatorial Optimization – Polyhedra and Efficiency | publisher = Springer | year = 2003 | location = | url = | doi = | id = | isbn = 978-3-540-44389-6 }}</ref> Egerváry generalized [[König's theorem (graph theory)|König's theorem]] to the case of [[Graph (mathematics)#Weighted graph|weighted graphs]].<ref name="Egervary1931">
{{Citation|first=Jenő|last=Egerváry|year=1931|title=Matrixok kombinatorius tulajdonságairól|language=Hungarian|trans_title=On combinatorial properties of matrices|journal=Matematikai és Fizikai Lapok|volume=38|pages=16–28}}
</ref> This contribution was translated and published in 1955 by [[Harold W. Kuhn]],<ref name="Kuhn1955a">{{citation|first=Harold W.|last=Kuhn|year=1955|title=On combinatorial properties of matrices|journal=Logistics Papers|publisher=George Washington University|volume=11|pages=1–11}}</ref> who also showed how to apply [[Dénes Kőnig|Kőnig]]'s and Egerváry's method to solve the [[assignment problem]]; the resulting algorithm has since been known as the "[[Hungarian method]]".<ref name="Kuhn1955b">{{Citation|first=Harold W.|last=Kuhn|year=1955|title=The Hungarian Method for the assignment problem|journal=Naval Research Logistics Quarterly|volume=2|pages=83–97}}</ref>
<!--
===Egerváry's Theorem===
Let <math>G=(V,E)</math> be a [[graph]] and let <math>w \in \mathbb{Z}^E_+</math>. A ''w-vertex cover'' is a vector <math>y \in \mathbb{Z}^V_+</math> such that <math>y_u+y_v \ge w_e</math> for every edge <math>(u,v)</math> of <math>G</math>. The ''size'' of a vector is the sum of its components.
 
Egerváry's Theorem can now be stated as follows. In any bipartite graph <math>G</math> with weight function <math>w:E \to \mathbb{Z}^E_+</math>, the maximum weight of a matching is equal to the minimum size of a ''w''-vertex cover.  
-->
 
==See also==
*[[König–Egerváry theorem]]
 
==Notes==
{{reflist|2}}
 
==References==
{{Refbegin}}
*{{Citation
|last=Rózsa
|first=Pál
|year=1984
|title=Jenő Egerváry – A great personality of the Hungarian mathematical school
|journal=Periodica Polytechnica Electrical Engineering
|volume=28
|pages=287–298
|publisher=Budapest University of Technology and Economics
|ref=harv
}}
*{{Citation
|last=Horváth
|first=János
|year=2005
|title=A panorama of Hungarian mathematics in the twentieth century
|volume=1
|publisher=Springer
|ref=harv
}}
*{{Citation
|last=Martello
|first=Silvano
|year=2010
|title=Jenő Egerváry: From the origins of the Hungarian algorithm to satellite communication
|journal=Central European Journal of Operations Research
|volume=18
|pages=47–58
|publisher=Springer
|ref=harv
}}
*{{Citation
|last=Rapcsák
|first=Tamás
|year=2010
|title=The life and works of Jenő Egerváry (1891–1958)
|journal=Central European Journal of Operations Research
|volume=18
|pages=59–71
|publisher=Springer
|ref=harv
}}
{{Refend}}
 
==External links==
*{{MathGenealogy |id=37271}}
*[http://www.cs.elte.hu/egres/www/mf_intro.html Egerváry Research Group on Combinatorial Optimization]
 
{{Authority control|VIAF=120203952}}
 
<!-- Metadata: see [[Wikipedia:Persondata]] -->
{{Persondata
|NAME=Egerváry, Jenő
|ALTERNATIVE NAMES=Egerváry, Eugene
|SHORT DESCRIPTION=Mathematician
|DATE OF BIRTH=April 16, 1891
|PLACE OF BIRTH=[[Debrecen]], [[Hungary]]
|DATE OF DEATH=30 November 1958
|PLACE OF DEATH=[[Budapest]], [[Hungary]]
}}
{{DEFAULTSORT:Egervary, Jeno}}
[[Category:Hungarian mathematicians]]
[[Category:20th-century mathematicians]]
[[Category:1891 births]]
[[Category:1958 deaths]]
[[Category:Mathematicians who committed suicide]]

Latest revision as of 03:15, 11 August 2014


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