Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fáry embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide an O(n) space,O(n logn) time algorithm to effect this embedding.Expand

We present an algorithm for constructing in O(n2) time a planar embedding of G mapping vertices to their assigned points and edges to polygonal curves with at least m/403 bends.Expand

We apply an idea of Szekely to prove a general upper bound on the number of incidences between a set m points and a set of n well-behaved curves in the plane.Expand

We show that a set of points in the plane determine O(n2 log n) triples that define the same angle α, and that for many angles α (including π 2 ) this bound is tight in the worst case.Expand

At most how many edges can an ordered graph ofn vertices have if it does not contain a fixed forbidden ordered subgraphH? It is not hard to give an asymptotically tight answer to this question,… Expand

We show that if a graph of v vertices can be drawn in the plane so that every edge crosses at most k> 0 others, then its number of edges cannot exceed 4.Expand

A colouring of the vertices of a hypergraph H is called conflict-free if each hyperedge E of H contains a vertex of ‘unique’ colour that does not get repeated in E.Expand