We show that every sufficiently large plane triangulation has a large collection of nested cycles that either are pairwise disjoint, or pairwise intersect in exactly one vertex, or pairwise intersect… (More)

4 A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that 5 each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing 6 number c̃r(G) of a graph… (More)

Zarankiewicz’s Conjecture (ZC) states that the crossing number cr(Km,n) equals Z(m,n) := bm2 cb m−1 2 cb n 2 cb n−1 2 c. Since Kleitman’s verification of ZC for K5,n (from which ZC for K6,n easily… (More)

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 crossingcriticality a property that… (More)