Zhihan Jin

collaborators

4 papers

math.CO2025

From small eigenvalues to large cuts, and Chowla's cosine problem

Zhihan Jin, Aleksa MilojeviÄ, IstvÃ¡n Tomon +1

We prove that every graph with average degree $d$ and smallest adjacency eigenvalue $∣ I^»_{n} ∣ \leq d^{3}$ contains a clique of size $d^{1 - O (I^^{3})}$ . A simple corollary of this yields the…

math.CO2025

Beyond the MaxCut problem in $H$ -free graphs

Zhihan Jin, Aleksa MilojeviÄ, IstvÃ¡n Tomon

In a recent breakthrough, Zhang proves that if $G$ is an $H$ -free graph with $m$ edges, then $G$ has a cut of size at least $m /2 + c_{H} m^{0.5001}$ , making a significant step towards a…

math.CO2025

Algebraic aspects of the polynomial Littlewood-Offord problem

Zhihan Jin, Matthew Kwan, Lisa Sauermann +1

Consider a degree- $d$ polynomial $f (I^¾_{1}, \dots, I^¾_{n})$ of independent Rademacher random variables $I^¾_{1}, \dots, I^¾_{n}$ . To what extent can $f (I^¾_{1}, \dots, I^¾_{n})$ concentrate on a single…

math.CO2025

Colouring random Hasse diagrams and box-Delaunay graphs

Zhihan Jin, Matthew Kwan, Lyuben Lichev

Fix $d \geq 2$ and consider a uniformly random set $P$ of $n$ points in $[0, 1]^{d}$ . Let $G$ be the Hasse diagram of $P$ (with respect to the coordinatewise partial order), or alterna…

From small eigenvalues to large cuts, and Chowla's cosine problem

Beyond the MaxCut problem in H-free graphs

Algebraic aspects of the polynomial Littlewood-Offord problem

Colouring random Hasse diagrams and box-Delaunay graphs

Beyond the MaxCut problem in $H$ -free graphs