English

On 4-Map Graphs and 1-Planar Graphs and their Recognition Problem

Computational Geometry 2015-09-14 v1

Abstract

We establish a one-to-one correspondence between 1-planar graphs and general and hole-free 4-map graphs and show that 1-planar graphs can be recognized in polynomial time if they are crossing-augmented, fully triangulated, and maximal 1-planar, respectively, with a polynomial of degree 120, 3, and 5, respectively.

Keywords

Cite

@article{arxiv.1509.03447,
  title  = {On 4-Map Graphs and 1-Planar Graphs and their Recognition Problem},
  author = {Franz J. Brandenburg},
  journal= {arXiv preprint arXiv:1509.03447},
  year   = {2015}
}
R2 v1 2026-06-22T10:54:26.745Z