Jian Wang

activity

20122026

most citedThe formula for Turán number of spanning linear forests

18 citations · 33 across the 23 of their papers we have counts for

collaborators

23 papers

math.CO2026

Intersecting families with covering number three II

Peter Frankl, Jian Wang

A family $F \subset (k [ n ])$ is called intersecting if $F \cap F^{'} \neq = \emptyset$ for all $F, F^{'} \in F$ . The covering number of a family $F$ is defi…

math.CO2023

A stability result for $C_{2 k + 1}$ -free graphs

Sijie Ren, Jian Wang, Shipeng Wang +1

A graph $G$ is called $C_{2 k + 1}$ -free if it does not contain any cycle of length $2 k + 1$ . In 1981, Haggkvist, Faudree and Schelp showed that every $n$ -vertex triangle-free graph wit…

math.CO2023

Four-vertex traces of finite sets

Peter Frankl, Jian Wang

Let $[n] = X_{1} \cup X_{2} \cup X_{3}$ be a partition with $⌊ \frac{n}{3} ⌋ \leq ∣ X_{i} ∣ \leq ⌈ \frac{n}{3} ⌉$ and define $\mathcal{G}=\{G\subset [n]\colon |G\cap X_i|\leq 1,…

math.CO2022★ 3 cited

Best possible bounds on the double-diversity of intersecting hypergraphs

Peter Frankl, Jian Wang

For a family $F \subset (k [ n ])$ and two elements $x, y \in [n]$ define $F (x ˉ, y ˉ) = {F \in F : x \in / F, y \in / F}$ . The double-di…

math.CO2022

Improved bounds concerning the maximum degree of intersecting hypergraphs

Peter Frankl, Jian Wang

For positive integers $n > k > t$ let $(k [ n ])$ denote the collection of all $k$ -subsets of the standard $n$ -element set $[n] = {1, \dots, n}$ . Subsets of $(k [ n ])$ are ca…

math.CO2022★ 1 cited

Intersecting families with covering number three

Peter Frankl, Jian Wang

We consider $k$ -graphs on $n$ vertices, that is, $F \subset (k [ n ])$ . A $k$ -graph $F$ is called intersecting if $F \cap F^{'} \neq = \emptyset$ for all $F,F'\in…

math.CO2022

A Product Version of the Hilton-Milner-Frankl Theorem

Peter Frankl, Jian Wang

Two families $F, G$ of $k$ -subsets of ${1, 2, \dots, n}$ are called non-trivial cross $t$ -intersecting if $∣ F \cap G ∣ \geq t$ for all $F\in \mathcal{F}, G\in \math…

math.CO2022

Counterexamples to Gerbner's Conjecture on Stability of Maximal $F$ -free Graphs

Jian Wang, Shipeng Wang, Weihua Yang

Let $F$ be an $(r + 1)$ -color critical graph with $r \geq 2$ , that is, $χ (F) = r + 1$ and there is an edge $e$ in $F$ such that $χ (F - e) = r$ . Gerbner recently conjectured that every $n$ -ver…

math.CO2022

Intersections and Distinct Intersections in Cross-intersecting Families

Peter Frankl, Jian Wang

Let $F, G$ be two cross-intersecting families of $k$ -subsets of ${1, 2, \dots, n}$ . Let $F \land G$ , $I (F, G)$ d…

math.CO2021

A Note on Minimum Degree Condition for Hamiltonian $(a, b)$ -Cycles in Hypergraphs

Jian Wang

Let $k, a, b$ be positive integers with $a + b = k$ . A $k$ -uniform hypergraph is called an $(a, b)$ -cycle if there is a partition $(A_{0}, B_{0}, A_{1}, B_{1}, \dots, A_{t - 1}, B_{t - 1})$ of the vertex…

math.CO2021

On the sum of sizes of overlapping families

Peter Frankl, Jian Wang

Let $A_{1}, \dots, A_{m}$ be families of $k$ -subsets of an $n$ -set. Suppose that one cannot choose pairwise disjoint edges from $s + 1$ distinct families. Subject to t…

math.CO2021★ 1 cited

The Generalized Turán Problem of Two Intersecting Cliques

Erica L. L. Liu, Jian Wang

For $s < r$ , let $B_{r, s}$ be the graph consisting of two copies of $K_{r}$ , which share exactly $s$ vertices. Denote by $e x (n, K_{r}, B_{r, s})$ the maximum number of copies of $K_{r}$ in…

math.CO2020

On the Maximum Number of Edges in Hypergraphs with Fixed Matching and Clique Number

Peter Frankl, Erica L. L. Liu, Jian Wang

For a $k$ -graph $F \subset (k [ n ])$ , the clique number of $F$ is defined to be the maximum size of a subset $Q$ of $[n]$ with $\binom{Q}{k}\subset \mathca…

math.CO2020★ 1 cited

A Stability Theorem for Maximal $C_{2 k + 1}$ -free Graphs

Jian Wang, Shipeng Wang, Weihua Yang +1

For any positive integer $k$ , we show that every maximal $C_{2 k + 1}$ -free graph with at least $n^{2} /4 - o (n^{3/2})$ edges contains an induced complete bipartite subgraph on $(1 - o (1)) n$ …

math.CO2020★ 1 cited

The Maximum Number of Cliques in Hypergraphs without Large Matchings

Erica L. L. Liu, Jian Wang

Let $[n]$ denote the set ${1, 2, \dots, n}$ and $F_{n, k, a}^{(r)}$ be an $r$ -uniform hypergraph on the vertex set $[n]$ with edge set consisting of all the $r$ -element…

math.CO2019★ 7 cited

Turán Problems for Vertex-disjoint Cliques in Multi-partite Hypergraphs

Erica L. L. Liu, Jian Wang

For two $s$ -uniform hypergraphs $H$ and $F$ , the Turán number $e x_{s} (H, F)$ is the maximum number of edges in an $F$ -free subgraph of $H$ . Let $s, r, k, n_{1}, \dots, n_{r}$ be integers…

math.CO2018

The maximum number of triangles in graphs without large linear forests

Xiuzhuan Duan, Jian Wang, Weihua Yang

Let $G$ be a graph on $n$ vertices. A linear forest is a graph consisting of vertex-disjoint paths and isolated vertices. A maximum linear forest of $G$ is a subgraph of $G$ with m…

math.CO2018

The Turán problem for a family of tight linear forests

Jian Wang, Weihua Yang

Let $F$ be a family of $r$ -graphs. The Turán number $e x_{r} (n; F)$ is defined to be the maximum number of edges in an $r$ -graph of order $n$ that is $F$ -…

math.CO2018★ 1 cited

The shifting method and generalized Turán number of matchings

Jian Wang

Given two graphs $T$ and $F$ , the maximum number of copies of $T$ in an $F$ -free graph on $n$ vertices is called the generalized Turán number, denoted by $e x (n, T, F)$ . When $T = K_{2}$ ,…

math.CO2018★ 18 cited

The formula for Turán number of spanning linear forests

Bo Ning, Jian Wang

Let $F$ be a family of graphs. The Turán number $e x (n; F)$ is defined to be the maximum number of edges in a graph of order $n$ that is $F$ -free. In 19…

math.CO2018

The Turán Number for Spanning Linear Forests

Jian Wang, Weihua Yang

For a set of graphs $F$ , the extremal number $e x (n; F)$ is the maximum number of edges in a graph of order $n$ not containing any subgraph isomorphic to some gra…

math.CO2017

Decycling Number of Linear Graphs of Trees

Jian Wang, Xirong Xu

The decycling number of a graph $G$ is the minimum number of vertices whose removal from $G$ results in an acyclic subgraph. It is known that determining the decycling number of a…

math.CO2012

Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

Shuming Zhou, Jian Wang, Xirong Xu +1

As the size of a multiprocessor system increases, processor failure is inevitable, and fault identification in such a system is crucial for reliable computing. The fault diagnosis…

Intersecting families with covering number three II

A stability result for C2k+1​-free graphs

Four-vertex traces of finite sets

Best possible bounds on the double-diversity of intersecting hypergraphs

Improved bounds concerning the maximum degree of intersecting hypergraphs

Intersecting families with covering number three

A Product Version of the Hilton-Milner-Frankl Theorem

Counterexamples to Gerbner's Conjecture on Stability of Maximal F-free Graphs

Intersections and Distinct Intersections in Cross-intersecting Families

A Note on Minimum Degree Condition for Hamiltonian (a,b)-Cycles in Hypergraphs

On the sum of sizes of overlapping families

The Generalized Turán Problem of Two Intersecting Cliques

On the Maximum Number of Edges in Hypergraphs with Fixed Matching and Clique Number

A Stability Theorem for Maximal C2k+1​-free Graphs

The Maximum Number of Cliques in Hypergraphs without Large Matchings

Turán Problems for Vertex-disjoint Cliques in Multi-partite Hypergraphs

The maximum number of triangles in graphs without large linear forests

The Turán problem for a family of tight linear forests

The shifting method and generalized Turán number of matchings

The formula for Turán number of spanning linear forests

The Turán Number for Spanning Linear Forests

Decycling Number of Linear Graphs of Trees

Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

A stability result for $C_{2 k + 1}$ -free graphs

Counterexamples to Gerbner's Conjecture on Stability of Maximal $F$ -free Graphs

A Note on Minimum Degree Condition for Hamiltonian $(a, b)$ -Cycles in Hypergraphs

A Stability Theorem for Maximal $C_{2 k + 1}$ -free Graphs