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}
}