Kuratowski's theorem: различия между версиями
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'''Kuratowski's theorem''' --- теорема Куратовского. | '''Kuratowski's theorem''' --- [[теорема Куратовского]]. | ||
'''Theorem'''. A graph <math>G</math> is planar iff it does not contain a | '''Theorem'''. A graph <math>G</math> is planar iff it does not contain a ''subdivision'' of <math>K_{5}</math> and <math>K_{3,3}</math>, i.e. iff it does not contain the ''minors'' <math>K_{5}</math> and <math>K_{3,3}</math>. | ||
''subdivision'' of <math>K_{5}</math> and <math>K_{3,3}</math>, i.e. iff it does not | |||
contain the ''minors'' <math>K_{5}</math> and <math>K_{3,3}</math>. | |||
The other name is '''Pontrjagin-Kuratowski's theorem'''. | The other name is '''[[Pontrjagin-Kuratowski's theorem|''Pontrjagin-Kuratowski's theorem'']]'''. | ||
Текущая версия от 20:11, 23 октября 2024
Kuratowski's theorem --- теорема Куратовского.
Theorem. A graph [math]\displaystyle{ G }[/math] is planar iff it does not contain a subdivision of [math]\displaystyle{ K_{5} }[/math] and [math]\displaystyle{ K_{3,3} }[/math], i.e. iff it does not contain the minors [math]\displaystyle{ K_{5} }[/math] and [math]\displaystyle{ K_{3,3} }[/math].
The other name is Pontrjagin-Kuratowski's theorem.