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 crk(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 Czabarka et al. that cr2(Q8)≤256 which we improve to cr2(Q8)≤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.
@article{arxiv.1711.01194,
title = {New Bounds on the Biplanar Crossing Number of Low-dimensional Hypercubes},
author = {Gregory Clark and Gwen Spencer},
journal= {arXiv preprint arXiv:1711.01194},
year = {2017}
}