Projects per year
Abstract
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 set of at least 328?2 points in the plane contains an empty pentagon or ? collinear points. This is optimal up to a constant factor since the (?  1) x (?  1) square lattice contains no empty pentagon and no ?collinear points. The previous best known bound was doubly exponential.
Original language  English 

Pages (fromto)  198209 
Number of pages  12 
Journal  SIAM Journal on Discrete Mathematics 
Volume  29 
Issue number  1 
DOIs  
Publication status  Published  2015 
Keywords
 Erd˝os problems
 discrete geometry
Projects
 1 Finished

The Structure and Geometry of Graphs
Australian Research Council (ARC)
1/01/08 → 31/12/13
Project: Research