A Note on the Weak Dirac Conjecture

Zeye Han

Abstract


We show that every set $\mathcal{P}$ of $n$ non-collinear points in the plane contains a point incident to at least $\lceil\frac{n}{3}\rceil+1$ of the lines determined by $\mathcal{P}$.

Keywords


Configurations of points; Incident-line-numbers; Weak Dirac Conjecture, Hirzebruch-type inequalities

Full Text: PDF