A Pseudoline Counterexample to the Strong Dirac Conjecture

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...

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Hauptverfasser: Lund, Ben D, Purdy, George B, Smith, Justin W
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Computer Science - Computational Geometry
Mathematics - Combinatorics
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Purdy, George B
Smith, Justin W
description 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.
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title A Pseudoline Counterexample to the Strong Dirac Conjecture
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