Klee–Wagon incidence conjecture

Prove or disprove that every finite set X of n non-collinear points in the plane contains an element incident with more than ⌈n/3⌉ lines spanned by X.

Background

The quantity t(X) is defined as the maximum number of lines spanned by X that are incident with a single point of X. Klee and Wagon proposed a lower bound of approximately one third of the number of points for this quantity.

Unlike the weak Dirac conjecture, which the paper states has been proved, the Klee–Wagon statement is presented without a resolution and is not addressed by the paper’s main theorem, which concerns configurations supported on three concurrent lines.