A Pseudoline Counterexample to the Strong Dirac Conjecture

Abstract

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.