Abstract
We draw the n-dimensional hypercube in the plane with \(\frac{5}{32}4^n - \lfloor \frac{n^2 + 1}{2} \rfloor 2^{n-2}\) crossings, which improves the previous best estimation and coincides with the long conjectured upper bound of Erdös and Guy.
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Faria, L., de Figueiredo, C.M.H., Sýkora, O., Vrt’o, I. (2003). An Improved Upper Bound on the Crossing Number of the Hypercube. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_20
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DOI: https://doi.org/10.1007/978-3-540-39890-5_20
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