Extending Erdős- Beck's theorem to higher dimensions

Abstract

Erdős-Beck theorem states that $n$ points in the plane with at most $n-x$ points collinear define at least $cxn$ lines for some positive constant $c$. In this paper, we will present two ways to extend this result to higher dimensions. Our result has application to point-hyperplane incidences and potential application to the point covering problem.

Cited by in corpus (2)

• Two theorems on point-flat incidences
• A note on the largest bipartite subgraph in point-hyperplane incidence graphs