I could prove that a four input butterfly network is planar. For that I simply drew it such that no two edges intersect. But I could not use the same approach for the 8-input butterfly network. So I tried doing the opposite by finding a subgraph of it which is a subdivision of either $K_{3,3}$ or $K_5$. Any help would be appreciated. Thanks.
2026-03-25 20:59:55.1774472395
Is a butterfly network on 8-inputs planar?
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It is, in fact, not planar. Here is a subgraph that is a subdivision of $K_{3,3}$. I colored the degree 3 vertices red to (hopefully) make it easier to see.