6 papers · 1 filter
A degree sum condition for the existence of a quasi 5-contractible edge in a quasi 5-connected graph
Shuai Kou, Chengfu Qin, Weihua Yang +2
An edge of a quasi -connected graph is said to be quasi -contractible if the contraction of the edge results in a quasi -connected graph. We show that every 5-connected gr…
A constructive characterization of uniformly 4-connected graphs
Xiang Chen, Shuai Kou, Chengfu Qin +2
A constructive characterization of the class of uniformly -connected graphs is presented. The characterization is based on the application of graph operations to appropriate ver…
Contractible Non-Edges in 3-Connected Graphs
Shuai Kou, Chengfu Qin, Weihua Yang +1
We call a pair of non-adjacent vertices in G a non-edge. Contraction of a non-edge {u, v} in G is the replacement of u and v with a single vertex z and then making all the vertices…
Contractible Subgraphs of Contraction Critically Quasi -Connected Graphs
Shuai Kou, Chengfu Qin, Weihua Yang
Let be a contraction critically quasi -connected graph on at least vertices. If there is a vertex such that or $G[N_{G}(x)]\c…
A note on -free graphs and -free graphs
Wenjian Jia, Shuai Kou, Chengfu Qin +1
Let and be the planar and non-planar graphs that obtained from the Octahedron by 3-splitting a vertex respectively. For , we prove that a 4…
Strengthened chain theorems for different versions of 4-connectivity
Guoli Ding, Chengfu Qin
The chain theorem of Tutte states that every 3-connected graph can be constructed from a wheel by repeatedly adding edges and splitting vertices. It is not difficult to prove…