Sijie Ren

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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.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

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…