Jacob Fox

collaborators

6 papers

math.CO2026

Three-color van der Waerden numbers grow super-exponentially

Jacob Fox, Zach Hunter

For $k$ sufficiently large, we show that there is a three-coloring of the first $2^{k (l o g^{*} k) /4}$ positive integers without any monochromatic $k$ -term arithmetic progressions. T…

math.CO2026

A note on the Alon-Saks-Seymour problem

Jacob Fox

Let $f (k)$ be the maximum possible chromatic number of a graph whose edge set can be partitioned into at most $k$ complete bipartite graphs. Alon, Saks, and Seymour conjectured tha…

math.CO2026

Finding blowups one vertex at a time

Jacob Fox, Yuval Wigderson, Yunkun Zhou

An influential theorem of Nikiforov states that if an $N$ -vertex graph $G$ contains at least $I^^{3} N^{h}$ copies of some fixed $h$ -vertex graph $H$ , then $G$ contains an $H$ -blowup of o…

cs.CG2026

Separators for intersection graphs of spheres

Jacob Fox, Jonathan Tidor

We prove the existence of optimal separators for intersection graphs of balls and spheres in any dimension $d$ . One of our results is that if an intersection graph of $n$ spheres i…

math.CO2026

Coloring small locally sparse degenerate graphs and related problems

Domagoj BradaÄ, Jacob Fox, Raphael Steiner +2

The classic upper bound on the chromatic number of $d$ -degenerate graphs is $d + 1$ , shown to be tight by complete graphs. A natural question is whether this bound remains tight if o…

math.CO2026

Color-avoiding directed paths in tournaments

Jacob Fox, Benny Sudakov, Yuval Wigderson

We study the following Ramsey-theoretic question: given a $q$ -coloring of the edges of a tournament, how long of a directed path can we guarantee whose edges avoid one of the color…