A Note on IC-Planar Graphs
Discrete Mathematics
2017-07-28 v1
Abstract
A graph is IC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share no common end vertex. IC-planarity specializes both NIC-planarity, which allows a pair of crossing edges to share at most one vertex, and 1-planarity, where each edge may be crossed at most once. We show that there are infinitely maximal IC-planar graphs with n vertices and 3n-5 edges and thereby prove a tight lower bound on the density of this class of graphs.
Cite
@article{arxiv.1707.08652,
title = {A Note on IC-Planar Graphs},
author = {Christian Bachmaier and Franz J. Brandenburg and Kathrin Hanauer},
journal= {arXiv preprint arXiv:1707.08652},
year = {2017}
}