Cubic planar bipartite graphs are dispersable
Combinatorics
2021-07-13 v1
Abstract
A graph is called dispersable if it has a book embedding in which each page has maximum degree 1 and the number of pages is the maximum degree. Bernhart and Kainen conjectured every k-regular bipartite graph is dispersable. Forty years later, Alam, Bekos, Gronemann, Kaufmann, and Pupyrev have disproved this conjecture, identifying nonplanar 3- and 4-regular bipartite graphs that are not dispersable. They also proved all cubic planar bipartite 3-connected graphs are dispersable and conjectured that the connectivity condition could be relaxed. We prove that every cubic planar bipartite multigraph is dispersable. A postscript is added which includes new references.
Keywords
Cite
@article{arxiv.2107.04728,
title = {Cubic planar bipartite graphs are dispersable},
author = {Paul C. Kainen and Shannon Overbay},
journal= {arXiv preprint arXiv:2107.04728},
year = {2021}
}