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Kuratowski's theorem
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Kuratowski's theorem
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
K
5
(the
complete graph
on five
vertices
) or of
K
3,3
(
complete bipartite graph
on six vertices, three of which connect to each of the other three, also known as the
utility graph
).
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