Characterizing graphs with crossing number at least 2


Recommended citation: Arroyo, A. and Richter, R. B. (2017), Characterizing Graphs with Crossing Number at Least 2. J. Graph Theory, 85: 738-746. doi:10.1002/jgt.22102

Our main result includes the following, slightly surprising, fact: a ‐connected nonplanar graph 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 with one containing and the other containing .