5 papers · 1 filter
Random Cayley graphs and random sumsets
Noga Alon, Huy Tuan Pham
We prove that any finite abelian group contains a collection of not too many subsets with a special structure, so that for every subset of with a small doubling, there…
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…
On monochromatic solutions to linear equations over the integers
Dingding Dong, Nitya Mani, Huy Tuan Pham +1
We study the number of monochromatic solutions to linear equations in a -coloring of . We show that any nontrivial linear equation has a constant fraction of sol…
Spread blow-up lemma with an application to perturbed random graphs
Rajko Nenadov, Huy Tuan Pham
Combining ideas of Pham, Sah, Sawhney, and Simkin on spread perfect matchings in super-regular bipartite graphs with an algorithmic blow-up lemma, we prove a spread version of the…
Short proof of the hypergraph container theorem
Rajko Nenadov, Huy Tuan Pham
We present a short and simple proof of the celebrated hypergraph container theorem of Balogh--Morris--Samotij and Saxton--Thomason. On a high level, our argument utilises the idea…