Curves, points, incidences and covering
Combinatorics
2025-11-05 v2 Computational Geometry
Discrete Mathematics
Abstract
Given a point set, mostly a grid in our case, we seek upper and lower bounds on the number of curves that are needed to cover the point set. We say a curve covers a point if the curve passes through the point. We consider such coverings by monotonic curves, lines, orthoconvex curves, circles, etc. We also study a problem that is converse of the covering problem -- if a set of points in the plane is covered by lines then can we say something about the configuration of the points?
Cite
@article{arxiv.2507.21758,
title = {Curves, points, incidences and covering},
author = {Arijit Bishnu and Mathew Francis and Pritam Majumder},
journal= {arXiv preprint arXiv:2507.21758},
year = {2025}
}