Light edges in 1‐planar graphs
Juan Liu, Yiqiao Wang, Weifan Wang · Journal of Graph Theory · 2022
Abstract A graph is 1‐planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1‐planar graph with minimum degree at least 3 contains an edge with such that one of the following holds: (1) and ; (2) and ; (3) and ; (4) and ; (5) . The upper bound on in each of the five items except the second is sharp.