Yan Wang

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math.CO2025

Path decompositions of Eulerian graphs

Yanan Chu, Yan Wang

Gallai's conjecture asserts that every connected graph on $n$ vertices can be decomposed into $\frac{n + 1}{2}$ paths. For general graphs (possibly disconnected), it was proved that…

math.CO2025

On the number of triangles in $K_{4}$ -free graphs

Jialin He, Jie Ma, Yan Wang +1

Erdős asked whether for any $n$ -vertex graph $G$ , the parameter $p^{*} (G) = min \sum_{i \geq 1} (∣ V (G_{i}) ∣ - 1)$ is at most $⌊ n^{2} /4 ⌋$ , where the minimum is taken over all edge…

math.CO2016

The Kelmans-Seymour conjecture III: 3-vertices in $K_{4}^{-}$

Dawei He, Yan Wang, Xingxing Yu

Let $G$ be a 5-connected nonplanar graph and let $x_{1}, x_{2}, y_{1}, y_{2} \in V (G)$ be distinct, such that $G [{x_{1}, x_{2}, y_{1}, y_{2}}] ≅ K_{4}^{-}$ and $y_{1} y_{2} \in / E (G)$ . We show that one of t…

Path decompositions of Eulerian graphs

On the number of triangles in K4​-free graphs

The Kelmans-Seymour conjecture III: 3-vertices in K4−​

On the number of triangles in $K_{4}$ -free graphs

The Kelmans-Seymour conjecture III: 3-vertices in $K_{4}^{-}$