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…
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…
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…
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…
Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs
Licheng Zhang, Shengxiang Lv, Yuanqiu Huang
The existence of Hamiltonian cycles in 1-planar graphs with higher connectivity has attracted considerable attention. Recently, the authors and Dong proved that 4-connected 1-plana…
The minimum size of 2-connected chordal bipartite graphs
Licheng Zhang, Yuanqiu Huang
A bipartite graph is chordal bipartite if every cycle of length at least six contains a chord. We determine the minimum size in 2-connected chordal bipartite graphs with given orde…
4-connected 1-planar chordal graphs are Hamiltonian-connected
Licheng Zhang, Yuanqiu Huang, Shengxiang Lv +1
Tutte proved that 4-connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar c…
On the sizes of generalized cactus graphs
Licheng Zhang, Yuanqiu Huang
A cactus is a connected graph in which each edge is contained in at most one cycle. We generalize the concept of cactus graphs, i.e., a -cactus is a connected graph in which eac…
The reducibility of optimal 1-planar graphs
Licheng Zhang, Yuanqiu Huang
A graph is reducible if it is the lexicographic product of two smaller non-trivial graphs. It is well-known a 1-planar graph with vertices has at most edges, and…