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

56 papers

math.CO2025

Immersions and Albertson's conjecture

Jacob Fox, Janos Pach, Andrew Suk

A graph is said to contain $K_{k}$ (a clique of size $k$ ) as a weak immersion if it has $k$ vertices, pairwise connected by edge-disjoint paths. In 1989, Lescure and Meyniel made the…

math.CO2024

When are off-diagonal hypergraph Ramsey numbers polynomial?

David Conlon, Jacob Fox, Benjamin Gunby +5

A natural open problem in Ramsey theory is to determine those $3$ -graphs $H$ for which the off-diagonal Ramsey number $r (H, K_{n}^{(3)})$ grows polynomially with $n$ . We make substan…

math.CO2024

Big line or big convex polygon

David Conlon, Jacob Fox, Xiaoyu He +3

Let $E S_{ℓ} (n)$ be the minimum $N$ such that every $N$ -element point set in the plane contains either $ℓ$ collinear members or $n$ points in convex position. We prove that th…

math.CO2024

Enumeration of intersection graphs of $x$ -monotone curves

Jacob Fox, Janos Pach, Andrew Suk

A curve in the plane is $x$ -monotone if every vertical line intersects it at most once. A family of curves are called pseudo-segments if every pair of them have at most one point i…

math.CO2024

On off-diagonal hypergraph Ramsey numbers

David Conlon, Jacob Fox, Benjamin Gunby +4

A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r (H, K_{n}^{(3)})$ of a fixed $3$ -uniform hypergraph $H$ versus the compl…

math.CO2024

A question of Erdős and Graham on Egyptian fractions

David Conlon, Jacob Fox, Xiaoyu He +4

Answering a question of Erdős and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive inte…

math.CO2023

A structure theorem for pseudo-segments and its applications

Jacob Fox, Janos Pach, Andrew Suk

We prove a far-reaching strengthening of Szemerédi's regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such a graph can be partitioned in…

math.CO2023

On cliques in three-dimensional dense point-line arrangements

Andrew Suk, Ji Zeng

As a variant of the celebrated Szemerédi--Trotter theorem, Guth and Katz proved that $m$ points and $n$ lines in $R^{3}$ with at most $n$ lines in a common plane must…

math.CO2023

On short edges in complete topological graphs

Andrew Suk

Let $h (n)$ be the minimum integer such that every complete $n$ -vertex simple topological graph contains an edge that crosses at most $h (n)$ other edges. In 2009, Kynčl and Valtr sh…

math.CO2023

Ramsey numbers of cliques versus monotone paths

Dhruv Mubayi, Andrew Suk

One formulation of the Erdos-Szekeres monotone subsequence theorem states that for any red/blue coloring of the edge set of the complete graph on ${1, 2, \dots, N}$ , there exist…

math.CO2022

Disjoint faces in simple drawings of the complete graph and topological Heilbronn problems

Alfredo Hubard, Andrew Suk

Given a complete simple topological graph $G$ , a $k$ -face generated by $G$ is the open bounded region enclosed by the edges of a non-self-intersecting $k$ -cycle in $G$ . Interesting…

math.CO2022

On higher dimensional point sets in general position

Andrew Suk, Ji Zeng

A finite point set in $R^{d}$ is in general position if no $d + 1$ points lie on a common hyperplane. Let $α_{d} (N)$ be the largest integer such that any set of $N$ points in…

math.CO2022

Hypergraph Ramsey numbers of cliques versus stars

David Conlon, Jacob Fox, Xiaoyu He +3

Let $K_{m}^{(3)}$ denote the complete $3$ -uniform hypergraph on $m$ vertices and $S_{n}^{(3)}$ the $3$ -uniform hypergraph on $n + 1$ vertices consisting of all $(2 n)$ edges incid…

math.CO2022★ 3 cited

Set-coloring Ramsey numbers via codes

David Conlon, Jacob Fox, Xiaoyu He +3

For positive integers $n, r, s$ with $r > s$ , the set-coloring Ramsey number $R (n; r, s)$ is the minimum $N$ such that if every edge of the complete graph $K_{N}$ receives a set of $s$ c…

math.CO2022

Unavoidable patterns in complete simple topological graphs

Andrew Suk, Ji Zeng

We show that every complete $n$ -vertex simple topological graph contains a topological subgraph on at least $(lo g n)^{1/4 - o (1)}$ vertices that is weakly isomorphic to the comple…

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 $i^{'} \neq = j^{'}$ …

math.CO2020

Cliques with many colors in triple systems

Dhruv Mubayi, Andrew Suk

Erdős and Hajnal constructed a 4-coloring of the triples of an $N$ -element set such that every $n$ -element subset contains 2 triples with distinct colors, and $N$ is double exponen…

math.CO2020

A note on the Erdős-Hajnal hypergraph Ramsey problem

Dhruv Mubayi, Andrew Suk, Emily Zhu

We show that there is an absolute constant $c > 0$ such that the following holds. For every $n > 1$ , there is a 5-uniform hypergraph on at least $2^{2^{c n^{1/4}}}$ vertices with inde…

math.CO2020

Hasse diagrams with large chromatic number

Andrew Suk, István Tomon

For every positive integer $n$ , we construct a Hasse diagram with $n$ vertices and chromatic number $Ω (n^{1/4})$ , which significantly improves on the previously known best construc…

math.CO2019

Bounded VC-dimension implies the Schur-Erdos conjecture

Jacob Fox, Janos Pach, Andrew Suk

In 1916, Schur introduced the Ramsey number $r (3; m)$ , which is the minimum integer $n$ such that for any $m$ -coloring of the edges of the complete graph $K_{n}$ , there is a monochrom…

Immersions and Albertson's conjecture

When are off-diagonal hypergraph Ramsey numbers polynomial?

Big line or big convex polygon

Enumeration of intersection graphs of x-monotone curves

On off-diagonal hypergraph Ramsey numbers

A question of Erdős and Graham on Egyptian fractions

A structure theorem for pseudo-segments and its applications

On cliques in three-dimensional dense point-line arrangements

On short edges in complete topological graphs

Ramsey numbers of cliques versus monotone paths

Disjoint faces in simple drawings of the complete graph and topological Heilbronn problems

On higher dimensional point sets in general position

Hypergraph Ramsey numbers of cliques versus stars

Set-coloring Ramsey numbers via codes

Unavoidable patterns in complete simple topological graphs

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

A positive fraction Erdos-Szekeres theorem and its applications

A note on visible islands

On the number of edges of separated multigraphs

Sunflowers in set systems of bounded dimension

Cliques with many colors in triple systems

A note on the Erdős-Hajnal hypergraph Ramsey problem

Hasse diagrams with large chromatic number

Bounded VC-dimension implies the Schur-Erdos conjecture

Enumeration of intersection graphs of $x$ -monotone curves