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Wagner's theorem (Theorem)
Theorem 1 (Wagner)   A graph is planar if and only if it contains neither $ K_5$ nor $ K_{3,3}$ as a minor, where $ K_5$ is the complete graph of order 5 and $ K_{3,3}$ is the complete bipartite graph of order 6.
Wagner's theorem is equivalent to Kuratowski's theorem.



"Wagner's theorem" is owned by Mathprof. [ full author list (2) | owner history (1) ]
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See Also: planar graph, Kuratowski's theorem

Keywords:  planar

Attachments:
proof of Wagner's theorem (Proof) by Ziosilvio
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Cross-references: Kuratowski's theorem, complete bipartite graph, order, complete graph, minor, contains, planar, graph
There are 4 references to this entry.

This is version 4 of Wagner's theorem, born on 2002-03-07, modified 2006-10-04.
Object id is 2771, canonical name is WagnersTheorem.
Accessed 4192 times total.

Classification:
AMS MSC: 05C99 (Combinatorics :: Graph theory :: Miscellaneous)
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