
arXiv: 2107.04728
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.
05C10, 05C62, 05C15, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
05C10, 05C62, 05C15, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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