7 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…
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…
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…