Dawei He

collaborators

3 papers

math.CO2016

The Kelmans-Seymour conjecture IV: a proof

Dawei He, Yan Wang, Xingxing Yu

A well known theorem of Kuratowski in 1932 states that a graph is planar if, and only if, it does not contain a subdivision of $K_{5}$ or $K_{3, 3}$ . Wagner proved in 1937 that if a g…

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…

math.CO2016

The Kelmans-Seymour conjecture II: 2-vertices in $K_{4}^{-}$

Dawei He, Yan Wang, Xingxing Yu

We use $K_{4}^{-}$ to denote the graph obtained from $K_{4}$ by removing an edge, and use $T K_{5}$ to denote a subdivision of $K_{5}$ . Let $G$ be a 5-connected nonplanar graph and $\{x_1,x_2…

The Kelmans-Seymour conjecture IV: a proof

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

The Kelmans-Seymour conjecture II: 2-vertices in K4−​

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

The Kelmans-Seymour conjecture II: 2-vertices in $K_{4}^{-}$