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I came across this post: How does the divisibility graphs work?

Where you can make a divisibility graph for any number n, using the method in the answer. Is it possible to have a divisibility graph that will always have a $K_5$ or $K_{3,3}$?

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tiscottt
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    What do you mean by "always"? Do you just want some divisibility graph that isn't planar? – Dustan Levenstein Dec 15 '15 at 14:09
  • I'm wondering if there is a set of graphs that will always be non-planar. For example the divisibility graph where n=6, and n=8 contain K3,3. Is there a rule or property that could tell me if a graph is non-planar or has K5 or K3,3 for all values of n? – tiscottt Dec 15 '15 at 14:26

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