1 citations · 1 across the 14 of their papers we have counts for
14 papers
On the Restricted Edge-Cuts of Optimal 1-Planar Graphs
Licheng Zhang, Zhangdong Ouyang, Yuanqiu Huang +1
The restricted edge-connectivity of a graph is the minimum size of an edge-cut whose removal leaves every component with at least two vertices. In 2024, Zhang et al. showed that th…
A note on optimal 2-planar graphs
Licheng Zhang, Yuanqiu Huang, Zhangdong Ouyang
In this note, we prove that every 4-connected optimal 2-planar graph is Hamiltonian-connected. Furthermore, we show that the 4-connectedness condition is sharp by constructing infi…
Maximal 1-plane graphs with the maximum number of crossings
Zhangdong Ouyang, Yuanqiu Huang, Licheng Zhang
A drawing of a graph in the plane is called 1-planar if each edge is crossed at most once. A graph together with a 1-planar drawing is a 1-plane graph. A 1-plane graph with exa…
The minimum size of maximal bipartite IC-plane graphs with given connectivity
Guiping Wang, Yuanqiu Huang, Zhangdong Ouyang +1
Recently, the problem of establishing bounds on the edge density of 1-planar graphs, including their subclass IC-planar graphs, has received considerable attention. In 2018, Angeli…
The minimum crossing number and minimum size of maximal 1-plane graphs with given connectivity
Zhangdong Ouyang, Yuanqiu Huang, Licheng Zhang +1
A 1-planar graph is a graph which has a drawing on the plane such that each edge is crossed at most once. If a 1-planar graph is drawn in that way, the drawing is called a {\it 1-p…
Determining the minimum size of maximal 1-plane graphs
Yuanqiu Huang, Zhangdong Ouyang, Licheng Zhang +1
A 1-plane graph is a graph together with a drawing in the plane in such a way that each edge is crossed at most once. A 1-plane graph is maximal if no edge can be added without vio…
The sharp upper bounds on the maximum degree and vertex-connectivity of claw-free 1-planar graphs
Licheng Zhang, Zhangdong Ouyang, Yuanqiu Huang
The complete bipartite graph is called a claw. The properties of claw-free graphs have attracted considerable attention, with research on claw-free planar graphs tracing…
The generalized 4-connectivity of godan graphs
Jing Wang, Yuanqiu Huang, Zhangdong Ouyang
The generalized -connectivity of a graph , denoted by , is the minimum number of internally edge disjoint -trees for any and . The general…
The generalized 4-connectivity of burnt pancake graphs
Jing Wang, Jiang Wu, Zhangdong Ouyang +1
The generalized -connectivity of a graph , denoted by , is the minimum number of internally edge disjoint -trees for any and . The general…
On the size of matchings in 1-planar graph with high minimum degree
Yuanqiu Huang, Zhangdong Ouyang, Fengming Dong
A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recen…
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 , in a connected multi-graph can be calculated by the Matrix-Tree theorem and Tutte's deletion-contraction…
On the sizes of bipartite 1-planar graphs
Yuanqiu Huang, Zhangdong Ouyang, Fengming Dong
A graph is called -planar if it admits a drawing in the plane such that each edge is crossed at most once. Let be a bipartite 1-planar graph with () vertices and…
New upper bounds for the crossing numbers of crossing-critical graphs
Zongpeng Ding, Zhangdong Ouyang, Yuanqiu Huang +1
A graph is {-crossing-critical} if , but for each edge , where is the crossing number of . It is known that for any $k…
Proving a conjecture on chromatic polynomials by counting the number of acyclic orientations
Fengming Dong, Jun Ge, Helin Gong +3
The chromatic polynomial of a graph of order can be expressed as , where is interpreted as the number of broken-cycle…