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A Pseudoline Counterexample to the Strong Dirac Conjecture (1202.3110v2)
Published 14 Feb 2012 in math.CO and cs.CG
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.