Jacob Fox

collaborators

4 papers

math.CO2026

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.CO2025

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.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.CO2025

Triangle Ramsey numbers of complete graphs

Jacob Fox, Jonathan Tidor, Shengtong Zhang

A graph is $H$ -Ramsey if every two-coloring of its edges contains a monochromatic copy of $H$ . Define the $F$ -Ramsey number of $H$ , denoted by $r_{F} (H)$ , to be the minimum number of…

Enumeration of intersection graphs of x-monotone curves

When are off-diagonal hypergraph Ramsey numbers polynomial?

Immersions and Albertson's conjecture

Triangle Ramsey numbers of complete graphs

Enumeration of intersection graphs of $x$ -monotone curves