Making a graph crossing-critical by multiplying its edges (Q1953450)

Summary: A graph is crossing-critical if the removal of any of its edges decreases its crossing number. This work is motivated by the following question: to what extent is crossing-criticality a property that is inherent to the structure of a graph, and to what extent can it be induced on a noncritical graph by multiplying (all or some of) its edges? It is shown that if a nonplanar graph \(G\) is obtained by adding an edge to a cubic polyhedral graph, and \(G\) is sufficiently connected, then \(G\) can be made crossing-critical by a suitable multiplication of edges.