1. The contractible subgraph of $5$-connected graphs
- Creator:
- Qin, Chengfu, Guo, Xiaofeng, and Yang, Weihua
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- 5-connected graph, contractible subgraph, and minor minimally $k$-connected
- Language:
- English
- Description:
- An edge $e$ of a $k$-connected graph $G$ is said to be $k$-removable if $G-e$ is still $k$-connected. A subgraph $H$ of a $k$-connected graph is said to be $k$-contractible if its contraction results still in a $k$-connected graph. A $k$-connected graph with neither removable edge nor contractible subgraph is said to be minor minimally $k$-connected. In this paper, we show that there is a contractible subgraph in a $5$-connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex of minor minimally $5$-connected graph is contained in some triangle.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public