Kuratowski's theorem
On forbidden subgraphs in planar graphs / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Kuratowski's theorem?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
For the point-set topology theorem, see Kuratowski's closure-complement problem.
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of (the complete graph on five vertices) or of (a complete bipartite graph on six vertices, three of which connect to each of the other three, also known as the utility graph).