Chen-Chvátal Conjecture in Graphs and Hypergraphs.

Abstract: It is well known that a set of n non-collinear points in the  Euclidean plane determines at least n distinct lines. In 2008, Chen  and Chvátal conjectured that this result extends to arbitrary finite  metric spaces with an appropriate definition of line. In this talk, we  present a survey of this conjecture, outlining known results in the  contexts of metric spaces, hypergraphs, and graphs