English

Embedding 1-Planar Graphs in Ten Pages

Discrete Mathematics 2023-12-27 v1

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.

Keywords

Cite

@article{arxiv.2312.15786,
  title  = {Embedding 1-Planar Graphs in Ten Pages},
  author = {Franz J. Brandenburg},
  journal= {arXiv preprint arXiv:2312.15786},
  year   = {2023}
}
R2 v1 2026-06-28T14:01:39.950Z