6 papers · 1 filter
-free graphs with many copies of
Cosmin Pohoata, Jonathan Tidor, Hung-Hsun Hans Yu
For every fixed integer , we construct an -vertex -free graph containing copies of . Combined with a simple counting argument, this show…
Triangle Ramsey numbers of complete graphs
Jacob Fox, Jonathan Tidor, Shengtong Zhang
A graph is -Ramsey if every two-coloring of its edges contains a monochromatic copy of . Define the -Ramsey number of , denoted by , to be the minimum number of…
More unit distances in arbitrary norms
Josef Greilhuber, Carl Schildkraut, Jonathan Tidor
For and any norm on , we prove that there exists a set of points that spans at least unit distances under this norm for every…
Uniform sets with few progressions via colorings
Mingyang Deng, Jonathan Tidor, Yufei Zhao
Ruzsa asked whether there exist Fourier-uniform subsets of with density and 4-term arithmetic progression (4-AP) density at most , for arbitrarily…
Multilevel polynomial partitioning and semialgebraic hypergraphs: regularity, Turán, and Zarankiewicz results
Jonathan Tidor, Hung-Hsun Hans Yu
We prove three main results about semialgebraic hypergraphs. First, we prove an optimal and oblivious regularity lemma. Fox, Pach, and Suk proved that the class of -uniform semi…
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…