Jian Wang

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20242026

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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…