A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...
We introduce the Turan problem for edge ordered graphs. We call a simple graph edge ordered, if its edges are linearly ordered. An isomorphism between edge ordered graphs must respect the edge order. A subgraph of an edge ordered graph is itself an edge or ...
An ordered graph H is a simple graph with a linear order on its vertex set. The corresponding Turan problem, first studied by Pach and Tardos, asks for the maximum number ex(
We show that any set of n points in general position in the plane determines n(1-o(1)) pairwise crossing segments. The best previously known lower bound, Omega(root n), was proved more than 25 years ago by Aronov, Erdos, Goddard, Kreitman, Krugerman, Pach, ...
Given a finite n-element set X, a family of subsets F subset of 2(X) is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if vertical bar F vertical bar > 2(n-1), then one can select vertical bar log n ...
