源于非常好覆盖图的局部极大稳定集拟阵
Local Maximum Stable Sets Greedoids Stemmed from Very Well-Covered Graphs
摘要：
图G中的最大稳定集是具有最大基数的稳定集。称S为G的一个局部极大稳定集，如果S是由S的闭邻域导出的子图的一个极大稳定集。如果存在图G=（V，E）使得它的局部极大稳定集族与（V，F）一致，则称（V，F）拟阵为局部极大稳定集拟阵。证明了森林T的族局部极大稳定集在其顶点集上构成一个广义拟阵。本文证明了如果G是一个非常好覆盖的图，那么它的局部极大稳定集族是一个拟序当且仅当G有唯一的完美匹配。
英文摘要：
A maximum stable set in a graph G is a stable set of maximum cardinality. S is called a local maximum stable set of G if S is a maximum stable set of the subgraph induced by the closed neighborhood of S. A greedoid (V,F) is called a local maximum stable set greedoid if there exists a graph G=(V,E) such that its family of local maximum stable sets coinsides with (V,F). It has been shown that the family local maximum stable sets of a forest T forms a greedoid on its vertex set. In this paper we demonstrate that if G is a very well-covered graph, then its family of local maximum stable sets is a greedoid if and only if G has a unique perfect matching.
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。
