论文标题
关键的等匹配图
Critical Equimatchable Graphs
论文作者
论文摘要
如果G的每个最大匹配均具有相同的基数，则图G是等效的。在本文中，我们研究了可匹配的图形，以使任何边缘的去除都会损害等于边缘临界的可匹配图（ECE-Graphs）。我们表明，除了两种简单的情况，即二分化ece-graphs，甚至集团，所有ECE编织都是2个关键因子关键的。因此，我们给出了具有连接性2的关键因子环境图形的表征。我们的结果为Levit和Mandrescu提出的关于覆盖良好的图表所提出的开放问题提供了部分答案，而没有脱落顶点。我们还介绍了可匹配的图表，以使任何顶点的去除都会损害等于匹配的性，称为临界值等匹配图（vce-graphs）。总而言之，我们启发了可匹配图的各种子类（包括ece-graphs and vce-graphs）之间的关系，并讨论了至少3个连接性的关键因子 - 关键因素图形的特性。
A graph G is equimatchable if every maximal matching of G has the same cardinality. In this paper, we investigate equimatchable graphs such that the removal of any edge harms the equimatchability, called edge-critical equimatchable graphs (ECE-graphs). We show that apart from two simple cases, namely bipartite ECE-graphs and even cliques, all ECE-graphs are 2-connected factor-critical. Accordingly, we give a characterization of factor-critical ECE-graphs with connectivity 2. Our result provides a partial answer to an open question posed by Levit and Mandrescu on the characterization of well-covered graphs with no shedding vertex. We also introduce equimatchable graphs such that the removal of any vertex harms the equimatchability, called vertex-critical equimatchable graphs (VCE-graphs). To conclude, we enlighten the relationship between various subclasses of equimatchable graphs (including ECE-graphs and VCE-graphs) and discuss the properties of factor-critical ECE-graphs with connectivity at least 3.
