Document Type
Article
Publication Date
6-2017
Publication Title
Bulletin of the Institute of Combinatorics and its Applications (BICA)
Abstract
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 [2] 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.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Rights
Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.
Version
Author's Accepted Manuscript
Recommended Citation
Clark, Gregory J. and Spencer, Gwen, "How Low Can You Go? New Bounds on the Biplanar Crossing Number of Low-dimensional Hypercubes" (2017). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/39
Comments
Peer reviewed accepted manuscript.