66 citations · 436 across the 112 of their papers we have counts for
9 papers · 2 filters
A proof of Tomescu's graph coloring conjecture
Jacob Fox, Xiaoyu He, Freddie Manners
In 1971, Tomescu conjectured that every connected graph on vertices with chromatic number has at most proper -colorings. Recently, Knox and Moha…
The Removal Lemma for Tournaments
Jacob Fox, Lior Gishboliner, Asaf Shapira +1
Suppose one needs to change the direction of at least edges of an -vertex tournament , in order to make it -free. A standard application of the regularity method sh…
Erdos-Hajnal conjecture for graphs with bounded VC-dimension
Jacob Fox, János Pach, Andrew Suk
The Vapnik-Chervonenkis dimension (in short, VC-dimension) of a graph is defined as the VC-dimension of the set system induced by the neighborhoods of its vertices. We show that ev…
A polynomial bound for the arithmetic -cycle removal lemma in vector spaces
Jacob Fox, László Miklós Lovász, Lisa Sauermann
For each , Green proved an arithmetic -cycle removal lemma for any abelian group . The best known bounds relating the parameters in the lemma for general are of…
Popular progression differences in vector spaces
Jacob Fox, Huy Tuan Pham
Green proved an arithmetic analogue of Szemerédi's celebrated regularity lemma and used it to verify a conjecture of Bergelson, Host, and Kra which sharpens Roth's theorem on three…
Erdős-Ginzburg-Ziv constants by avoiding three-term arithmetic progressions
Jacob Fox, Lisa Sauermann
For a finite abelian group , the Erdős-Ginzburg-Ziv constant is the smallest such that every sequence of (not necessarily distinct) elements of has…