Dawei He

activity

20102016

most citedThe Kelmans-Seymour conjecture I: special separations

1 citations · 1 across the 5 of their papers we have counts for

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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…

math.CO2015★ 1 cited

The Kelmans-Seymour conjecture I: special separations

Dawei He, Yan Wang, Xingxing Yu

Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of $K_{5}$ . This conjecture was proved by Ma and Yu for gra…

math.CO2010

On the number of a SDRs of a valued (t,n)-family

Dawei He, Changhong Lu

A system of distinct representatives (SDR) of a family $F = (A_{1}, \dots, A_{n})$ is a sequence $(x_{1}, \dots, x_{n})$ of $n$ distinct elements with $x_{i} \in A_{i}$ for $1 \leq i \leq n$ .…

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 I: special separations

On the number of a SDRs of a valued (t,n)-family

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

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