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Article

Making a Graph Crossing-Critical by Multiplying its Edges

Electronic Journal of Combinatorics. 2013. Vol. 20. No. 1. P. 1-14.
Beaudou L., Hernández-Vélez C., Salazar G.

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.