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arXiv · 1707.08652

A Note on IC-Planar Graphs

Christian Bachmaier·Franz J. Brandenburg·Kathrin Hanauer
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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.

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Christian Bachmaier, Franz J. Brandenburg, Kathrin Hanauer. 2017-07-26. A Note on IC-Planar Graphs. https://arxiv.org/abs/1707.08652

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