A Pseudoline Counterexample to the Strong Dirac Conjecture
  We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of n pseudolines has no member incident to more than 4n/9 points of intersection. This shows the "Strong Dirac" conjecture to be false for pseudolines.   We also raise a number of open problems relating to possible differences between the structure of incidences between points and lines versus the structure of incidences between points and pseudolines. 
Ben D. Lund, George B. Purdy, Justin W. Smith
math.CO cs.CG