优化正则图的限制边连通性的最小度条件(英文)
Minimum Degree Condition for the Optimization of Restricted Edge Connectivity of Regular Graphs
Abstract
限制边割将连通图分离成不含孤立点的不连通图 ,如果最小限制边割只能分离孤立边 ,则称图G是超级限制边连通的 .证明了如果k >|G|/ 2 +1,那么k正则连通图G是超级限制边连通的 ,k的下界在一定程度上是不可改进的 . Restricted edge cut separates a connected graph into a disconnected one without isolated vertex.Graph G is super restricted edge connected if no subgraph but an isolated edge can be separated by any minimum restricted edge cut.It is proved that k regular connected graph G is super restricted edge connected if k>|G|/2+1 . The lower bound on k is exemplified to be sharp to some extent.