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There are three general lower bound techniques for the crossing numbers of graphs: the Crossing Lemma, the bisection method and the embedding method. Inthis contribution, we present their adaptations to the minor crossing number. Using the adapted bounds, we improve on the known bounds on the minor ...

Let ▫$S$▫ be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of ▫$S$▫ with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probability that ▫$S$▫ defines a pair of crossing edges ...