2017/07/26 by Christian Bachmaier, Bachmaier, Christian, Franz J. Brandenburg +3
Computer Science · #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1707.08652
openalex publication_date 2017/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.