Bulletin of the Institute of Combinatorics and its Applications (BICA)
In this note we provide an improved upper bound on the biplanar crossing number of the 8-dimensional hypercube. The k-planar crossing number of a graph cr k ( G) is the number of crossings required when every edge of G must be drawn in one of k distinct planes. It was shown in  that cr 2 ( Q 8 ) ≤ 256 which we improve to cr 2 ( Q 8 ) ≤ 128. Our approach highlights the relationship between symmetric drawings and the study of k-planar crossing numbers. We conclude with several open questions concerning this relationship.
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Clark, Gregory J. and Spencer, Gwen, "How Low Can You Go? New Bounds on the Biplanar Crossing Number of Low-dimensional Hypercubes" (2017). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.