Andrew Suk

activity

20102025

most citedErdos-Szekeres-type theorems for monotone paths and convex bodies

48 citations · 110 across the 37 of their papers we have counts for

collaborators

Showing 2021Show all

5 papers · 1 filter

math.CO2021

Quasiplanar Graphs, String Graphs, and the Erdos-Gallai Problem

Jacob Fox, Janos Pach, Andrew Suk

An $r$ -quasiplanar graph is a graph drawn in the plane with no $r$ pairwise crossing edges. Let $s \geq 3$ be an integer and $r = 2^{s}$ . We prove that there is a constant $C$ such tha…

math.CO2021

A positive fraction Erdos-Szekeres theorem and its applications

Andrew Suk, Ji Zeng

A famous theorem of Erdos and Szekeres states that any sequence of $n$ distinct real numbers contains a monotone subsequence of length at least $n$ . Here, we prove a positiv…

math.CO2021

A note on visible islands

Sophie Leuchtner, Carlos M. Nicolas, Andrew Suk

Given a finite point set $P$ in the plane, a subset $S \subseteq P$ is called an island in $P$ if $co n v (S) \cap P = S$ . We say that $S \subset P$ is a visible island if the points i…

math.CO2021

On the number of edges of separated multigraphs

Jacob Fox, Janos Pach, Andrew Suk

We prove that the number of edges of a multigraph $G$ with $n$ vertices is at most $O (n^{2} lo g n)$ , provided that any two edges cross at most once, parallel edges are noncrossing, a…

math.CO2021

Sunflowers in set systems of bounded dimension

Jacob Fox, Janos Pach, Andrew Suk

Given a family $F$ of $k$ -element sets, $S_{1}, \dots, S_{r} \in F$ form an {\em $r$ -sunflower} if $S_{i} \cap S_{j} = S_{i^{'}} \cap S_{j^{'}}$ for all $i \neq = j$ and $i^{'} \neq = j^{'}$ …