Characterizing Graphs with Crossing Number at Least 2
Alan Arroyo, R. Bruce Richter · Journal of Graph Theory · 2016
Abstract Our main result includes the following, slightly surprising, fact: a 4‐connected nonplanar graph G has crossing number at least 2 if and only if, for every pair of edges having no common incident vertex, there are vertex‐disjoint cycles in G with one containing e and the other containing f.