66 citations · 436 across the 112 of their papers we have counts for
9 papers · 1 filter
Sparse graphs with no polynomial-sized anticomplete pairs
Maria Chudnovsky, Jacob Fox, Alex Scott +2
A graph is "-free" if it has no induced subgraph isomorphic to . A conjecture of Conlon, Fox and Sudakov states that for every graph , there exists such that in ever…
Towards the linear arboricity conjecture
Asaf Ferber, Jacob Fox, Vishesh Jain
The linear arboricity of a graph , denoted by , is the minimum number of edge-disjoint linear forests (i.e. forests in which every connected component is a path) i…
A Completion of the Proof of the Edge-statistics Conjecture
Jacob Fox, Lisa Sauermann
For given integers and with , Alon, Hefetz, Krivelevich and Tyomkyn formulated the following conjecture: When sampling a -vertex subset uniform…
Online Ramsey Numbers and the Subgraph Query Problem
David Conlon, Jacob Fox, Andrey Grinshpun +1
The -online Ramsey game is a combinatorial game between two players, Builder and Painter. Starting from an infinite set of isolated vertices, Builder draws an edge on each t…
Finding Cliques in Social Networks: A New Distribution-Free Model
Jacob Fox, Tim Roughgarden, C. Seshadhri +2
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the propert…
Towards Erdos-Hajnal for graphs with no 5-hole
Maria Chudnovsky, Jacob Fox, Alex Scott +2
The Erdos-Hajnal conjecture says that for every graph there exists such that for every -free graph with vertices, and this is still op…