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arXiv · 2507.21758

Curves, points, incidences and covering

Arijit Bishnu·Mathew Francis·Pritam Majumder
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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 $n^2$ points in the plane is covered by $n$ lines then can we say something about the configuration of the points?

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Arijit Bishnu, Mathew Francis, Pritam Majumder. 2026-09-03. Curves, points, incidences and covering. https://arxiv.org/abs/2507.21758

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