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.
@article{10_37236_4015,
author = {Ben Lund and George B. Purdy and Justin W. Smith},
title = {A pseudoline counterexample to the strong {Dirac} conjecture},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {2},
doi = {10.37236/4015},
zbl = {1300.05048},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4015/}
}
TY - JOUR
AU - Ben Lund
AU - George B. Purdy
AU - Justin W. Smith
TI - A pseudoline counterexample to the strong Dirac conjecture
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4015/
DO - 10.37236/4015
ID - 10_37236_4015
ER -
%0 Journal Article
%A Ben Lund
%A George B. Purdy
%A Justin W. Smith
%T A pseudoline counterexample to the strong Dirac conjecture
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4015/
%R 10.37236/4015
%F 10_37236_4015
Ben Lund; George B. Purdy; Justin W. Smith. A pseudoline counterexample to the strong Dirac conjecture. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/4015
