Jun Gao

collaborators

5 papers

math.CO2026

Rational codegree TurÃ¡n density of hypergraphs

Jun Gao, Oleg Pikhurko, Mingyuan Rong +1

Let $H$ be a $k$ -graph (i.e. a $k$ -uniform hypergraph). Its minimum codegree $I^´_{k - 1} (H)$ is the largest integer $t$ such that every $(k - 1)$ -subset of $V (H)$ is contained in at le…

math.CO2025

On cliques in hypergraphs

Jun Gao

We prove that for any $k \geq 3$ , every $k$ -uniform hypergraph on $n$ vertices contains at most $n - I ¨ (1)$ different sizes of cliques (maximal complete subgraphs). In particular, t…

math.CO2025

Covering large-dimensional Euclidean spaces by random translates of a given convex body

Boris Bukh, Jun Gao, Xizhi Liu +2

Determining the minimum density of a covering of $R^{n}$ by Euclidean unit balls as $n \to \infty$ is a major open problem, with the best known results being the lower bound…

math.MG2025

New upper bound for lattice covering by spheres

Jun Gao, Xizhi Liu, Oleg Pikhurko +1

We show that there exists a lattice covering of $R^{n}$ by Eucledian spheres of equal radius with density $O (n ln^{2} n)$ as $n \to \infty$ , where \begin{align*} Î²:=…

math.CO2025

Strong Ramsey game on two boards

Jiangdong Ai, Jun Gao, Zixiang Xu +1

The strong Ramsey game $R (B, H)$ is a two-player game played on a graph $B$ , referred to as the board, with a target graph $H$ . In this game, two players, $P_{1}$ …