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arXiv · 2312.15786

Embedding 1-Planar Graphs in Ten Pages

Franz J. Brandenburg
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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. 2023-12-25. Embedding 1-Planar Graphs in Ten Pages. https://arxiv.org/abs/2312.15786

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