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by definition, a subgraph is a $K_{3,3}$ configuration if it can be obtained from a $K_{3,3}$ by adding vertices in the middle of some edges. But I still don't understand the definition. Can anyone show me an example of $K_{3,3}$ configuration and how to find it?
$\endgroup$1 Answer
$\begingroup$Here's a couple of pictures of $K_{3,3}$:
and adding some vertices for a $K_{3,3}$ configuration:
where you can recover the $K_{3,3}$ , eliminating degree-2 vertices and joining the adjacent vertices (and also eliminating any duplicate edges, which don't figure in this example).
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