Yi Zhao

activity

20082022

most citedMinimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs

36 citations · 131 across the 28 of their papers we have counts for

collaborators

28 papers

math.CO2022

On subgraphs of tripartite graphs

Abhijeet Bhalkikar, Yi Zhao

Bollobás, Erdős, and Szemerédi [Discrete Math 13 (1975), 97--107] investigated a tripartite generalization of the Zarankiewicz problem: what minimum degree forces a tripartite grap…

math.CO2022

Independence number of hypergraphs under degree conditions

Vojtěch Rödl, Marcelo Sales, Yi Zhao

A well-known result of Ajtai et al. from 1982 states that every $k$ -graph $H$ on $n$ vertices, with girth at least five, and average degree $t^{k - 1}$ contains an independent set of…

math.CO2021★ 3 cited

Complete subgraphs in a multipartite graph

Allan Lo, Andrew Treglown, Yi Zhao

In 1975 Bollobás, Erd\H os, and Szemerédi asked the following question: given positive integers $n, t, r$ with $2 \leq t \leq r - 1$ , what is the largest minimum degree $δ (G)$ among all…

math.CO2021

Shadows of 3-uniform hypergraphs under a minimum degree condition

Zoltán Füredi, Yi Zhao

We prove a minimum degree version of the Kruskal--Katona theorem: given $d \geq 1/4$ and a triple system $F$ on $n$ vertices with minimum degree at least $d (2 n)$ , we obtain asym…

math.CO2020★ 6 cited

Improved bounds on the Ramsey number of fans

Guantao Chen, Xiaowei Yu, Yi Zhao

For a given graph $H$ , the Ramsey number $r (H)$ is the minimum $N$ such that any 2-edge-coloring of the complete graph $K_{N}$ yields a monochromatic copy of $H$ . Given a positive in…

math.CO2020

Minimum degree thresholds for Hamilton $(k /2)$ -cycles in $k$ -uniform hypergraphs

Hiep Han, Jie Han, Yi Zhao

For any even integer $k \geq 6$ , integer $d$ such that $k /2 \leq d \leq k - 1$ , and sufficiently large $n \in (k /2) N$ , we find a tight minimum $d$ -degree condition that guarantees t…

math.CO2019

Existence thresholds and Ramsey properties of random posets

Victor Falgas-Ravry, Klas Markström, Andrew Treglown +1

Let $P (n)$ denote the power set of $[n]$ , ordered by inclusion, and let $P (n, p)$ denote the random poset obtained from $P (n)$ by retaining each element…

math.CO2019★ 5 cited

Turán number of disjoint triangles in 4-partite graphs

Jie Han, Yi Zhao

Let $k \geq 2$ and $n_{1} \geq n_{2} \geq n_{3} \geq n_{4}$ be integers such that $n_{4}$ is sufficiently larger than $k$ . We determine the maximum number of edges of a 4-partite graph with parts of…

math.CO2019

Triangle-degrees in graphs and tetrahedron coverings in 3-graphs

Victor Falgas--Ravry, Klas Markström, Yi Zhao

We investigate a covering problem in $3$ -uniform hypergraphs ( $3$ -graphs): given a $3$ -graph $F$ , what is $c_{1} (n, F)$ , the least integer $d$ such that if $G$ is an $n$ -vertex $3$ -gr…

math.CO2019

Vertex degree sums for matchings in 3-uniform hypergraphs

Yi Zhang, Yi Zhao, Mei Lu

Let $n, s$ be positive integers such that $n$ is sufficiently large and $s \leq n /3$ . Suppose $H$ is a 3-uniform hypergraph of order $n$ . If $H$ contains no isolated vertex and $deg(…

math.CO2018★ 11 cited

Hamiltonicity in randomly perturbed hypergraphs

Jie Han, Yi Zhao

For integers $k \geq 3$ and $1 \leq ℓ \leq k - 1$ , we prove that for any $α > 0$ , there exist $ε > 0$ and $C > 0$ such that for sufficiently large $n \in (k - ℓ) N$ , the union of a $k…

math.CO2017★ 2 cited

Vertex degree sums for perfect matchings in 3-uniform hypergraphs

Yi Zhang, Yi Zhao, Mei Lu

We determine the minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-graph without isolated vertex. More precisely, suppose that $H$ is a 3-uniform h…

math.CO2017

A degree version of the Hilton--Milner theorem

Peter Frankl, Jie Han, Hao Huang +1

An intersecting family of sets is trivial if all of its members share a common element. Hilton and Milner proved a strong stability result for the celebrated Erdős--Ko--Rado theore…

math.CO2016★ 6 cited

Codegree conditions for tiling complete $k$ -partite $k$ -graphs and loose cycles

Wei Gao, Jie Han, Yi Zhao

Given two $k$ -graphs ( $k$ -uniform hypergraphs) $F$ and $H$ , a perfect $F$ -tiling (or an $F$ -factor) in $H$ is a set of vertex disjoint copies of $F$ that together cover the vertex…

math.CO2016★ 4 cited

Matchings in $k$ -partite $k$ -uniform Hypergraphs

Jie Han, Chuanyun Zang, Yi Zhao

For $k \geq 3$ and $ε > 0$ , let $H$ be a $k$ -partite $k$ -graph with parts $V_{1}, \dots, V_{k}$ each of size $n$ , where $n$ is sufficiently large. Assume that for each $i \in [k]$ , every $(k…

math.CO2016★ 2 cited

New Upper Bound for Sums of Dilates

Albert Bush, Yi Zhao

For $λ \in Z$ , let $λ \cdot A = {λa : a \in A}$ . Suppose $r, h \in Z$ are sufficiently large and comparable to each other. We prove that if $∣ A + A ∣ \leq K ∣ A ∣$ and…

math.CO2016★ 4 cited

Degree versions of the Erdos-Ko-Rado Theorem and Erdos hypergraph matching conjecture

Hao Huang, Yi Zhao

We use an algebraic method to prove a degree version of the celebrated Erd\H os-Ko-Rado theorem: given $n > 2 k$ , every intersecting $k$ -uniform hypergraph $H$ on $n$ vertices contain…

math.CO2016★ 2 cited

Asymptotics of Ramsey numbers of double stars

Sergey Norin, Yue Ru Sun, Yi Zhao

A double star $S (n, m)$ is the graph obtained by joining the center of a star with $n$ leaves to a center of a star with $m$ leaves by an edge. Let $r (S (n, m))$ denote the Ramsey num…

math.CO2015

Codegree thresholds for covering 3-uniform hypergraphs

Victor Falgas-Ravry, Yi Zhao

Given two 3-uniform hypergraphs F and G, we say that G has an F-covering if we can cover V(G) by copies of F. The minimum codegree of G is the largest integer d such that every pai…

math.CO2015★ 5 cited

Recent advances on Dirac-type problems for hypergraphs

Yi Zhao

A fundamental question in graph theory is to establish conditions that ensure a graph contains certain spanning subgraphs. Two well-known examples are Tutte's theorem on perfect ma…

math.CO2015★ 1 cited

Forbidding Hamilton cycles in uniform hypergraphs

Jie Han, Yi Zhao

For $1 \leq d \leq ℓ < k$ , we give a new lower bound for the minimum $d$ -degree threshold that guarantees a Hamilton $ℓ$ -cycle in $k$ -uniform hypergraphs. When $k \geq 4$ and $d< \e…

math.CO2015★ 31 cited

Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs

Jie Han, Chuanyun Zang, Yi Zhao

Given positive integers $a \leq b \leq c$ , let $K_{a, b, c}$ be the complete 3-partite 3-uniform hypergraph with three parts of sizes $a, b, c$ . Let $H$ be a 3-uniform hypergraph on $n$ …

math.CO2014★ 5 cited

Minimum degree thresholds for bipartite graph tiling

Albert Bush, Yi Zhao

For any bipartite graph $H$ , we determine a minimum degree threshold for a balanced bipartite graph $G$ to contain a perfect $H$ -tiling. We show that this threshold is best possibl…

math.CO2013★ 3 cited

Minimum vertex degree threshold for $C_{4}^{3}$ -tiling

Jie Han, Yi Zhao

We prove that the vertex degree threshold for tiling $\C_4^3$ (the 3-uniform hypergraph with four vertices and two triples) in a 3-uniform hypergraph on $n \in 4 N$ vertices…

On subgraphs of tripartite graphs

Independence number of hypergraphs under degree conditions

Complete subgraphs in a multipartite graph

Shadows of 3-uniform hypergraphs under a minimum degree condition

Improved bounds on the Ramsey number of fans

Minimum degree thresholds for Hamilton (k/2)-cycles in k-uniform hypergraphs

Existence thresholds and Ramsey properties of random posets

Turán number of disjoint triangles in 4-partite graphs

Triangle-degrees in graphs and tetrahedron coverings in 3-graphs

Vertex degree sums for matchings in 3-uniform hypergraphs

Hamiltonicity in randomly perturbed hypergraphs

Vertex degree sums for perfect matchings in 3-uniform hypergraphs

A degree version of the Hilton--Milner theorem

Codegree conditions for tiling complete k-partite k-graphs and loose cycles

Matchings in k-partite k-uniform Hypergraphs

New Upper Bound for Sums of Dilates

Degree versions of the Erdos-Ko-Rado Theorem and Erdos hypergraph matching conjecture

Asymptotics of Ramsey numbers of double stars

Codegree thresholds for covering 3-uniform hypergraphs

Recent advances on Dirac-type problems for hypergraphs

Forbidding Hamilton cycles in uniform hypergraphs

Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs

Minimum degree thresholds for bipartite graph tiling

Minimum vertex degree threshold for C43​-tiling

Minimum degree thresholds for Hamilton $(k /2)$ -cycles in $k$ -uniform hypergraphs

Codegree conditions for tiling complete $k$ -partite $k$ -graphs and loose cycles

Matchings in $k$ -partite $k$ -uniform Hypergraphs

Minimum vertex degree threshold for $C_{4}^{3}$ -tiling