kuratowski’s principle
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Any network that is non-planar must contain \(K_5\) or \(K_{3,3}\) or a network obtained from one of these by replacing a link with a path.
The computation is carried out with enumerating all 5 node/6 node configurations and testing if they would form \(K_5\) or \(K_{3,3}\), so it is intractable.