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引用次数: 0
摘要
循环是唯一两个不相邻的顶点形成一个顶点切口的 2 连接图。我们通过证明对于每一个整数（k\ge 3\）都存在一个满足以下三个条件的唯一图 G 来推广这一事实：（1）G 是 k 连接的；（2）G 的独立数大于 k；（3）任何心率为 k 的独立集都是 G 的顶点切分。我们还考虑了用边缘代替独立集的问题。
Cycles are the only 2-connected graphs in which any two nonadjacent vertices form a vertex cut. We generalize this fact by proving that for every integer \(k\ge 3\) there exists a unique graph G satisfying the following three conditions: (1) G is k-connected; (2) the independence number of G is greater than k; (3) any independent set of cardinality k is a vertex cut of G. However, the edge version of this result does not hold. We also consider the problem when replacing independent sets by the periphery.
期刊介绍：
Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.
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