A Pseudoline Counterexample to the Strong Dirac Conjecture
Combinatorics
2014-01-14 v2 Computational Geometry
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.
Cite
@article{arxiv.1202.3110,
title = {A Pseudoline Counterexample to the Strong Dirac Conjecture},
author = {Ben D. Lund and George B. Purdy and Justin W. Smith},
journal= {arXiv preprint arXiv:1202.3110},
year = {2014}
}