General Lower Bounds for the Minor Crossing Number of Graphs
There are three general lower bound techniques for the crossing numbers of graphs: the Crossing Lemma, the bisection method and the embedding method. In this contribution, we present their adaptations to the minor crossing number. Using the adapted bounds, we improve on the known bounds on the minor crossing number of hypercubes. We also point out relations of the minor crossing number to string graphs and establish a lower bound for the standard crossing number in terms of Randi index.
minor crossing number crossing number hypercube string graphs graph minor