Embedding 1-Planar Graphs in Ten Pages (2312.15786v1)

Published 25 Dec 2023 in cs.DM

Abstract: Every planar graph has a 4-page book embedding and this bound is tight. We show that every 1-planar graph, which is a graph that admits a drawing with at most one crossing per edge, has a 10-page book embedding. In addition, four pages are sometimes necessary and always sufficient if the planar skeleton, obtained from a 1-planar drawing by removing all crossed edges, has a Hamiltonian cycle.

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Franz J. Brandenburg

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