Jie Han

activity

20142026

collaborators

11 papers

math.CO2026

Exact minimum co-degree conditions for $ℓ$ -Hamiltonicity in hypergraphs

Luyining Gan, Jie Han, Huan Xu

Suppose $1 \leq ℓ < k$ such that $(k - ℓ) ∤ k$ . Given an $n$ -vertex $k$ -uniform hypergraph $H$ , for all $k /2 < ℓ < 3 k /4$ and sufficiently large $n\in (k-\ell)\mathbb N…

math.CO2025

Clique-factors in graphs with low $K_{ℓ}$ -independence number

Ming Chen, Jie Han, Donglei Yang

Given $r \in N$ with $r \geq 4$ , we show that there exists $n_{0} \in N$ such that for every $n \geq n_{0}$ , every $n$ -vertex graph $G$ with $δ(G)\geq (\frac{1}{2}+o(1))n…

math.CO2025

Transversal packings in families of percolated hypergraphs

Jie Han, Jie Hu, Shunan Wei +1

Let $F$ be a strictly $1$ -balanced $k$ -graph on $s$ vertices with $t$ edges and $δ_{F, d}^{T}$ be the infimum of $δ > 0$ such that for every $α > 0$ and sufficiently large $n\in \mathbb{N…

math.CO2025

Supersaturation of odd linear cycles

Lirong Deng, Jie Han, Jiaxi Nie +1

An $r$ -uniform linear cycle of length $ℓ$ , denoted by $C_{ℓ}^{r}$ , is an $r$ -graph with $ℓ$ edges $e_{1}, e_{2}, \dots, e_{ℓ}$ where $e_i=\{v_{(r-1)(i-1)},v_{(r-1)(i-1)+1},\dots…

math.CO2024

On the thresholds of degenerate hypergraphs

Yu Chen, Jie Han, Haoran Luo

An $n$ -vertex $k$ -uniform hypergraph $G$ is $(d, α)$ -degenerate if $m_{1} (G) \leq d$ and there exists a constant $ε > 0$ such that for every subset $U \subseteq V (G)$ with siz…

math.CO2024

Ramsey--Dirac theory for bounded degree hypertrees

Jie Han, Seonghyuk Im, Jaehoon Kim +1

Ramsey--Turán theory considers Turán type questions in Ramsey-context, asking for the existence of a small subgraph in a graph $G$ where the complement $G$ lacks an appr…

math.CO2024

Turán number of complete multipartite graphs in multipartite graphs

Jie Han, Yi Zhao

In this paper we study a multi-partite version of the Erdős--Stone theorem. Given integers $r < k$ and $t \geq 1$ , let $ex_{k} (n, K_{r + 1} (t))$ be the maximum number of edges of $K…

math.CO2024

Hamiltonicity of Sparse Pseudorandom Graphs

Asaf Ferber, Jie Han, Dingjia Mao +1

We show that every $(n, d, λ)$ -graph contains a Hamilton cycle for sufficiently large $n$ , assuming that $d \geq lo g^{6} n$ and $λ \leq c d$ , where $c = \frac{1}{70000}$ . This significant…

math.CO2023

A robust version of the multipartite Hajnal--Szemerédi theorem

Jie Han, Jie Hu, Donglei Yang

In this note we show the following strengthening of a multipartite version of the Hajnal--Szemerédi theorem. For an integer $r \geq 3$ and $γ > 0$ , there exists a constant $C$ such t…

math.CO2023

The threshold for powers of tight Hamilton cycles in random hypergraphs

Yulin Chang, Jie Han, Lin Sun

We investigate the occurrence of powers of tight Hamilton cycles in random hypergraphs. For every $r \geq 3$ and $k \geq 1$ , we show that there exists a constant $C > 0$ such that if $…

math.CO2014

Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs

Jie Han, Yi Zhao

For $1 \leq ℓ < k /2$ , we show that for sufficiently large $n$ , every $k$ -uniform hypergraph on $n$ vertices with minimum codegree at least $\frac{n}{2 ( k - ℓ )}$ contains a Hamilton…

Exact minimum co-degree conditions for ℓ-Hamiltonicity in hypergraphs

Clique-factors in graphs with low Kℓ​-independence number

Transversal packings in families of percolated hypergraphs

Supersaturation of odd linear cycles

On the thresholds of degenerate hypergraphs

Ramsey--Dirac theory for bounded degree hypertrees

Turán number of complete multipartite graphs in multipartite graphs

Hamiltonicity of Sparse Pseudorandom Graphs

A robust version of the multipartite Hajnal--Szemerédi theorem

The threshold for powers of tight Hamilton cycles in random hypergraphs

Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs

Exact minimum co-degree conditions for $ℓ$ -Hamiltonicity in hypergraphs

Clique-factors in graphs with low $K_{ℓ}$ -independence number