关于图的最小临界独立集的结构
On the Structure of the Minimum Critical Independent Set of a Graph
摘要：
设G=（V，E）.一个集合S是独立的，如果S中没有两个顶点相邻。数字d（X）= |X| -|N（X）|是X的差，并且如果d（A）= max{d（I）：I是独立集}，则独立集A是临界的。让我们回想一下，ker（G）是所有临界独立集的交集，而core（G）是所有最大独立集的交集。最近，人们建立了ker（G）是core（G）的一个子集，这对任何图都成立，而相应的等式对二部图也成立。本文给出了ker（G）的各种结构性质。本文的主要结果是：ker（G）等于所有包含极小独立集的正差并。
英文摘要：
Let G=(V,E). A set S is independent if no two vertices from S are adjacent. The number d(X)= |X|-|N(X)| is the difference of X, and an independent set A is critical if d(A) = max{d(I):I is an independent set}. Let us recall that ker(G) is the intersection of all critical independent sets, and core(G) is the intersection of all maximum independent sets. Recently, it was established that ker(G) is a subset of core(G) is true for every graph, while the corresponding equality holds for bipartite graphs. In this paper we present various structural properties of ker(G). The main finding claims that ker(G) is equal to the union of all inclusion minimal independent sets with positive difference.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
