10 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…
The maximum number of -cliques of 7-connected 1-planar graphs
Yuanqiu Huang, Licheng Zhang
In 2023, Gollin, Hendrey, Methuku, Tompkins and Zhang determined the maximum number of cliques in general 1-planar graphs with order . Their extremal examples have connectivity…
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…
Extremal 1-planar graphs without k-cliques
Licheng Zhang, Yuanqiu Huang, Fengming Dong
In 2016, Dowden initiated the study of planar Turán-type problems, which has since attracted considerable attention. Recently, Bekos et al. proved that every -free -planar…
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…