12 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…
On the maximum number of edges of k-cacti
Licheng Zhang, Yuanqiu Huang
A cactus is a graph in which every edge lies on at most one cycle. In 2024, Zhang and Huang generalized this concept to the -cactus, defined as a graph in which every edge lies…
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 density of maximal IC-plane graphs and maximal NIC-plane graphs
Zongpeng Ding, Yuanqiu Huang, Fengming Dong +2
In this paper, we show that any maximal IC-plane graph of order has at least edges, and any maximal NIC-plane graph of order…