6 papers · 1 filter
A note on arithmetic progressions with restricted differences
David Conlon, Jacob Fox, Huy Tuan Pham
In this note, we show how to adapt Tao's slice rank method to extend the Ellenberg--Gijswijt theorem on cap sets to the problem of forbidding arithmetic progressions with restricte…
A question of ErdÅs and Graham on Egyptian fractions
David Conlon, Jacob Fox, Xiaoyu He +4
Answering a question of ErdÅs and Graham, we show that for each fixed positive rational number the number of ways to write as a sum of reciprocals of distinct positive int…
On the clique number of random Cayley graphs and related topics
David Conlon, Jacob Fox, Huy Tuan Pham +1
We prove that a random Cayley graph on a group of order has clique number with high probability. This bound is best possible up to the constant factor f…
The largest subgraph without a forbidden induced subgraph
Jacob Fox, Rajko Nenadov, Huy Tuan Pham
We initiate the systematic study of the following Turán-type question. Suppose is a graph with vertices such that the edge density between any pair of subsets of vertices…
Big line or big convex polygon
David Conlon, Jacob Fox, Xiaoyu He +3
Let be the minimum such that every -element point set in the plane contains either collinear members or points in convex position. We prove that th…
Equivalence between ErdÅs-Hajnal and polynomial Rödl and Nikiforov conjectures
Matija BuciÄ, Jacob Fox, Huy Tuan Pham
It is well-known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical ErdÅs-Hajnal conj…