Editing Kuratowski's theorem (section)

==History==
[[Kazimierz Kuratowski]] published his theorem in 1930.<ref>{{citation|first=Kazimierz|last=Kuratowski|author-link=Kazimierz Kuratowski|year=1930|url=http://matwbn.icm.edu.pl/ksiazki/fm/fm15/fm15126.pdf|title=Sur le problème des courbes gauches en topologie|journal=Fund. Math.|volume=15|pages=271–283|doi=10.4064/fm-15-1-271-283 |language=French}}.</ref> The theorem was independently proved by [[Orrin Frink]] and [[Paul Althaus Smith|Paul Smith]], also in 1930,<ref>{{citation
 | last1 = Frink | first1 = Orrin | author-link1 = Orrin Frink
 | last2 = Smith | first2 = Paul A. | author-link2 = Paul Althaus Smith
 | title = Irreducible non-planar graphs
 | journal = Bulletin of the AMS
 | volume = 36
 | pages = 214
 | year = 1930 }}</ref> but their proof was never published.  The special case of [[cubic graph|cubic]] planar graphs (for which the only minimal forbidden subgraph is <math>K_{3,3}</math>) was also independently proved by [[Karl Menger]] in 1930.<ref>{{citation
 | last = Menger | first = Karl | author-link = Karl Menger
 | title = Über plättbare Dreiergraphen und Potenzen nichtplättbarer Graphen
 | journal =  Anzeiger der Akademie der Wissenschaften in Wien
 | volume = 67
 | pages = 85–86
 | year = 1930}}</ref>
Since then, several new proofs of the theorem have been discovered.<ref>{{citation
 | last = Thomassen | first = Carsten | author-link = Carsten Thomassen (mathematician)
 | doi = 10.1002/jgt.3190050304
 | issue = 3
 | journal = Journal of Graph Theory
 | mr = 625064
 | pages = 225–241
 | title = Kuratowski's theorem
 | volume = 5
 | year = 1981}}.</ref>

In the [[Soviet Union]], Kuratowski's theorem was known as either the '''Pontryagin–Kuratowski theorem''' or the '''Kuratowski–Pontryagin theorem''',<ref>{{citation
 | last1 = Burstein | first1 = Michael
 | doi = 10.1016/0095-8956(78)90024-2
 | title = Kuratowski-Pontrjagin theorem on planar graphs
 | journal = Journal of Combinatorial Theory, Series B
 | volume = 24
 | pages = 228–232
 | year = 1978| issue = 2
 | doi-access = 
 }}</ref>
as the theorem was reportedly proved independently by [[Lev Pontryagin]] around 1927.<ref>{{citation
 | last1 = Kennedy | first1 = John W.
 | last2 = Quintas | first2 = Louis V.
 | last3 = Sysło | first3 = Maciej M.
 | doi = 10.1016/0315-0860(85)90045-X
 | title = The theorem on planar graphs
 | journal = Historia Mathematica
 | volume = 12
 | pages = 356–368
 | year = 1985| issue = 4
 | doi-access = free
 }}</ref>
However, as Pontryagin never published his proof, this usage has not spread to other places.<ref>{{citation|title=Graphs & Digraphs|edition=5th|first1=Gary|last1=Chartrand|author1-link=Gary Chartrand|first2=Linda|last2=Lesniak|first3=Ping|last3=Zhang|author3-link=Ping Zhang (graph theorist)|publisher=CRC Press|year=2010|isbn=9781439826270|page=237|url=https://books.google.com/books?id=K6-FvXRlKsQC&pg=PA237}}.</ref>