Zhangdong Ouyang

activity

20182021

collaborators

4 papers

math.CO2021

Express the number of spanning trees in term of degrees

Fengming Dong, Jun Ge, Zhangdong Ouyang

It is well-known that the number of spanning trees, denoted by $τ (G)$ , in a connected multi-graph $G$ can be calculated by the Matrix-Tree theorem and Tutte's deletion-contraction…

math.CO2020

On the sizes of bipartite 1-planar graphs

Yuanqiu Huang, Zhangdong Ouyang, Fengming Dong

A graph is called $1$ -planar if it admits a drawing in the plane such that each edge is crossed at most once. Let $G$ be a bipartite 1-planar graph with $n$ ( $\geq 4$ ) vertices and…

math.CO2020

New upper bounds for the crossing numbers of crossing-critical graphs

Zongpeng Ding, Zhangdong Ouyang, Yuanqiu Huang +1

A graph $G$ is { $k$ -crossing-critical} if $cr (G) \geq k$ , but $cr (G ∖ e) < k$ for each edge $e \in E (G)$ , where $cr (G)$ is the crossing number of $G$ . It is known that for any $k…

math.CO2018

Proving a conjecture on chromatic polynomials by counting the number of acyclic orientations

Fengming Dong, Jun Ge, Helin Gong +3

The chromatic polynomial $P (G, x)$ of a graph $G$ of order $n$ can be expressed as $i = 1 \sum n (- 1)^{n - i} a_{i} x^{i}$ , where $a_{i}$ is interpreted as the number of broken-cycle…