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I'm probably doing something stupid but I can't seem to think of a way to draw $Q_5$ with $cr(Q_5) = 56 $. In this paper the author says drawing a hypercube graph with $\leq56$ edge crossings is easy (look under section 3 topological invariants) Could anyone give me an idea of how to get 56 edge crossings. I always end up getting 60 when I draw it.

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3 Answers

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I found the article where this fact is shown. However, I can't access it in it's entirety without paying... Here it is It shows the first page, but everything else is kind of blurred out. It does not have the same layout as Ed Pegg's answer. I will try and edit this with a picture of the graph, but in the meantime, if maybe you have access to the above article, you can see it for yourself.

EDIT: Here is a drawing of $Q_5$ with 56 crossings. I believe it is still conjectured that $cr(Q_5)=56$

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Here's a cleaner version of the 56 crossing. The left and right wrap around.

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I'm running into 60 as well. I'd also like to see the 56.

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