44 citations · 51 across the 11 of their papers we have counts for
4 papers · 1 filter
On the general position subset selection problem
Michael S. Payne, David R. Wood
Let be the maximum integer such that every set of points in the plane with at most collinear contains a subset of points with no three collinear.…
Empty pentagons in point sets with collinearities
János Barát, Vida Dujmović, Gwenaël Joret +5
An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite s…
Progress on Dirac's Conjecture
Michael S. Payne, David R. Wood
In 1951, Gabriel Dirac conjectured that every set P of n non-collinear points in the plane contains a point in at least n/2-c lines determined by P, for some constant c. The follow…
Which point sets admit a k-angulation?
Michael S. Payne, Jens M. Schmidt, David R. Wood
For k >= 3, a k-angulation is a 2-connected plane graph in which every internal face is a k-gon. We say that a point set P admits a plane graph G if there is a straight-line drawin…