Adam Sheffer

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20232026

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3 papers · 1 filter

math.CO2026

The Minimum Number of Plane Graphs for Sets with Small Hulls

Alice Chen, Tara Saini, Adam Sheffer +1

Let $P$ be a set of $n$ points in $R^{2}$ , with a convex hull of size $O (n / lo g n)$ . We prove that $Ω (12.2 4^{n})$ plane graphs can be drawn on $P$ , the fir…

math.CO2024

Expected degrees in random plane graphs

Neely Lovvorn, Oscar Murillo-Espinoza, Adam Sheffer

We prove that, for every set of $n$ points $P$ in $R^{2}$ , a random plane graph drawn on $P$ is expected to contain less than $n /10.18$ isolated vertices…

math.CO2023

Structural Szemerédi-Trotter for Lattices and their Generalizations

Shival Dasu, Adam Sheffer, Junxuan Shen

We completely characterize point--line configurations with $Θ (n^{4/3})$ incidences when the point set is a section of the integer lattice. This can be seen as the main special case…