Jian Wang

activity

20242026

collaborators

11 papers

math.CO2026

On the chromatic profile for tripartite graphs and beyond

Bo Ning, Jian Wang, Yisai Xue

Let $H$ be a graph and let $δ_{χ} (H, r)$ denote the infimum of $c$ such that every $H$ -free graph with minimum degree at least $c n$ is $r$ -colorable. The \textit{chromatic profile} of…

math.CO2026

Nearly Erdős-Ko-Rado theorems

Gyula O. H. Katona, Jian Wang

If a family $F$ of $k$ -element subsets of an $n$ -element set is pairwise intersecting, $2 k \leq n$ then $∣ F ∣ \leq (k - 1 n - 1)$ holds by the celebrated Erdős-…

math.CO2025

Andr{á}sfai--Erdős--Sós theorem under max-degree constraints

Xizhi Liu, Sijie Ren, Jian Wang

We establish the following strengthening of the celebrated Andr{á}sfai--Erdős--Sós theorem: If $G$ is an $n$ -vertex $K_{r + 1}$ -free graph whose minimum degree $δ (G)$ and maximum deg…

math.CO2025

Hypergraph Turán problem of the generalized triangle with bounded matching number

Jian Wang, Wenbin Wang, Weihua Yang

Let $H$ be a 3-graph on $n$ vertices. The matching number $ν (H)$ is defined as the maximum number of disjoint edges in $H$ . The generalized triangle $…

math.CO2025

Largest $3$ -uniform set systems with VC-dimension $2$

Jian Wang, Zixiang Xu, Shengtong Zhang

We determine the largest size of $3$ -uniform set systems on $[n]$ with VC-dimension $2$ for all $n$ .

math.CO2025

Gallai-Schur Triples and Related Problems

Yaping Mao, Aaron Robertson, Jian Wang +2

Schur's Theorem states that, for any $r \in Z^{+}$ , there exists a minimum integer $S (r)$ such that every $r$ -coloring of ${1, 2, \dots, S (r)}$ admits a monochromatic solutio…

math.CO2025

A note on the maximum diversity of intersecting families in the symmetric group

Jian Wang, Jimeng Xiao

Let $S_{n}$ be the symmetric group on the set $[n] := {1, 2, \dots, n}$ . A family $F \subset S_{n}$ is called intersecting if for every $σ, π \in F$ …

math.CO2024

Positive codegree Andrásfai--Erdős--Sós theorem for the generalized triangle

Xizhi Liu, Sijie Ren, Jian Wang

The celebrated Andrásfai--Erdős--Sós Theorem from 1974 shows that every $n$ -vertex triangle-free graph with minimum degree greater than $2 n /5$ must be bipartite. We establish a pos…

math.CO2024

Andrásfai--Erdős--Sós theorem for the generalized triangle

Xizhi Liu, Sijie Ren, Jian Wang

The celebrated Andrásfai--Erdős--Sós Theorem from 1974 shows that every $n$ -vertex triangle-free graph with minimum degree greater than $2 n /5$ must be bipartite. Its extensions to…

math.CO2024

Triangle-free Graphs with Large Minimum Common Degree

Jian Wang, Weihua Yang, Fan Zhao

Let $G$ be a graph. For $x \in V (G)$ , let $N (x) = {y \in V (G) : x y \in E (G)}$ . The minimum common degree of $G$ , denoted by $δ_{2} (G)$ , is defined as the minimum of $|N(x)\cap N(y…

math.CO2024

Extremal triangle-free graphs with chromatic number at least four

Sijie Ren, Jian Wang, Shipeng Wang +1

Let $G$ be an $n$ -vertex triangle-free graph. The celebrated Mantel's theorem showed that $e (G) \leq ⌊ \frac{n ^{2}}{4} ⌋$ . In 1962, Erdős (together with Gallai), and indepen…

On the chromatic profile for tripartite graphs and beyond

Nearly Erdős-Ko-Rado theorems

Andr{á}sfai--Erdős--Sós theorem under max-degree constraints

Hypergraph Turán problem of the generalized triangle with bounded matching number

Largest 3-uniform set systems with VC-dimension 2

Gallai-Schur Triples and Related Problems

A note on the maximum diversity of intersecting families in the symmetric group

Positive codegree Andrásfai--Erdős--Sós theorem for the generalized triangle

Andrásfai--Erdős--Sós theorem for the generalized triangle

Triangle-free Graphs with Large Minimum Common Degree

Extremal triangle-free graphs with chromatic number at least four

Largest $3$ -uniform set systems with VC-dimension $2$