Sufficiency for the Existence of R_m-EDGE CUT
- 数学科学－已发表论文 
Rm 边割是这样一种边割 ,它将连通图分割为各分支的阶都不小于m的不连通图 .设G是一个阶不小于 2m的连通图 .用c(G)表示G的周长 (即G中最长圈的长度 ) ,如果c(G)≥m +1,那么G含有Rm 边割 ,而且周长c的下界在一定程度上是不可改进的R m-edge cut is such an edge cut that separates a connected graph into a disconnected one with no component having order less than m. Let G be a connected graph with order at least 2m . Write c(G) for the circumference of graph G , i.e., the length of the longest cycle in G . It is proved in this paper that graph G contains R m-edge cuts if c(G) ≥m+1. The lower bound of c(G) is sharp to some extent.