Jie Han

A parameterized algorithm for $K_{r}$ -factors in graphs of high minimum degree

Luyining Gan, Jie Han, Jie Hu

A $K_{r}$ -factor of a graph $G$ is a collection of vertex-disjoint $r$ -cliques covering $V (G)$ . We prove the following algorithmic version of the classical Hajnal--Szemerédi Theorem…

On powers of Hamilton cycles in Ramsey-Turán Theory

Ming Chen, Jie Han, Yantao Tang +1

We prove that for $r \in N$ with $r \geq 2$ and $μ > 0$ , there exist $α > 0$ and $n_{0}$ such that for every $n \geq n_{0}$ , every $n$ -vertex graph $G$ with $δ(G)\geq \left(1-\fr…

Large $Y_{3, 2}$ -tilings in 3-uniform hypergraphs

Jie Han, Lin Sun, Guanghui Wang

Let $Y_{3, 2}$ be the 3-graph with two edges intersecting in two vertices. We prove that every 3-graph $H$ on $n$ vertices with at least $ \max \left \{ \binom{4αn}{3}, \binom{n…

Spanning trees in graphs without large bipartite holes

Jie Han, Jie Hu, Lidan Ping +3

We show that for any $ε > 0$ and $Δ \in N$ , there exists $α > 0$ such that for sufficiently large $n$ , every $n$ -vertex graph $G$ satisfying that $δ(G)\geq\varepsilon…

Dirac-type Problem of Rainbow matchings and Hamilton cycles in Random Graphs

Asaf Ferber, Jie Han, Dingjia Mao

Given a family of graphs $G_{1}, \dots, G_{n}$ on the same vertex set $[n]$ , a rainbow Hamilton cycle is a Hamilton cycle on $[n]$ such that each $G_{c}$ contributes exactly one edge. We…

math.CO2022★ 1 cited

Spanning trees in sparse expanders

Jie Han, Donglei Yang

Given integers $n \geq Δ \geq 2$ , let $T (n, Δ)$ be the collection of all $n$ -vertex trees with maximum degree at most $Δ$ . A question of Alon, Krivelevich and Sudakov in 2007…

Finding matchings in dense hypergraphs

Jie Han, Peter Keevash

We consider the algorithmic decision problem that takes as input an $n$ -vertex $k$ -uniform hypergraph $H$ with minimum codegree at least $m - c$ and decides whether it has a matching…

$H$ -factors in graphs with small independence number

Ming Chen, Jie Han, Guanghui Wang +1

Let $H$ be an $h$ -vertex graph. The vertex arboricity $a r (H)$ of $H$ is the least integer $r$ such that $V (H)$ can be partitioned into $r$ parts and each part induces a forest in $…

math.CO2022★ 1 cited

Clique-factors in graphs with sublinear $ℓ$ -independence number

Jie Han, Ping Hu, Guanghui Wang +1

Given a graph $G$ and an integer $ℓ \geq 2$ , we denote by $α_{ℓ} (G)$ the maximum size of a $K_{ℓ}$ -free subset of vertices in $V (G)$ . A recent question of Nenadov and Pehova…

On the Keevash-Knox-Mycroft Conjecture

Luyining Gan, Jie Han

Given $1 \leq ℓ < k$ and $δ \geq 0$ , let $PM (k, ℓ, δ)$ be the decision problem for the existence of perfect matchings in $n$ -vertex $k$ -uniform hypergraphs with minimum $\el…

cs.IT2021

Structural Entropy of the Stochastic Block Models

Jie Han, Tao Guo, Qiaoqiao Zhou +3

With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data i…

Embedding clique-factors in graphs with low $ℓ$ -independence number

Fan Chang, Jie Han, Jaehoon Kim +2

The following question was proposed by Nenadov and Pehova and reiterated by Knierim and Su: Given integers $ℓ, r$ and $n$ with $n \in r N$ , is it true that every $n$ -verte…

Tiling multipartite hypergraphs in Quasi-random Hypergraphs

Laihao Ding, Jie Han, Shumin Sun +2

Given $k \geq 2$ and two $k$ -graphs ( $k$ -uniform hypergraphs) $F$ and $H$ , an \emph{ $F$ -factor} in $H$ is a set of vertex disjoint copies of $F$ that together covers the vertex set o…

Transversal Hamilton cycle in hypergraph systems

Yangyang Cheng, Jie Han, Bin Wang +2

A $k$ -graph system $H = {H_{i}}_{i \in [m]}$ is a family of not necessarily distinct $k$ -graphs on the same $n$ -vertex set $V$ and a $k$ -graph $H$ on $V$ is said to be $\textb…

Large $Y_{k, b}$ -tilings and Hamilton $ℓ$ -cycles in $k$ -uniform hypergraphs

Luyining Gan, Jie Han, Lin Sun +1

Let $Y_{3, 2}$ be the $3$ -uniform hypergraph with two edges intersecting in two vertices. Our main result is that any $n$ -vertex 3-uniform hypergraph with at least $\binom{n}{3} - \…

math.CO2021★ 3 cited

$F$ -factors in Quasi-random Hypergraphs

Laihao Ding, Jie Han, Shumin Sun +2

Given $k \geq 2$ and two $k$ -graphs ( $k$ -uniform hypergraphs) $F$ and $H$ , an $F$ -factor in $H$ is a set of vertex-disjoint copies of $F$ that together covers the vertex set of $H$ .…

Matching of given sizes in hypergraphs

Yulin Chang, Huifen Ge, Jie Han +1

For all integers $k, d$ such that $k \geq 3$ and $k /2 \leq d \leq k - 1$ , let $n$ be a sufficiently large integer {\rm(}which may not be divisible by $k$ {\rm)} and let $s\le \lfloor n/…