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.
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 and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/39
Comments
Peer reviewed accepted manuscript.