Title: Integer k-matching preclusion of graphs Show Chinese title

Title: 图的整数k匹配预clusion

Abstract: As a generalization of matching preclusion number of a graph, we provide the (strong) integer $k$-matching preclusion number, abbreviated as $MP^{k}$ number ($SMP^{k}$ number), which is the minimum number of edges (vertices and edges) whose deletion results in a graph that has neither perfect integer $k$-matching nor almost perfect integer $k$-matching. In this paper, we show that when $k$ is even, the ($SMP^{k}$) $MP^{k}$ number is equal to the (strong) fractional matching preclusion number. We obtain a necessary condition of graphs with an almost-perfect integer $k$-matching and a relational expression between the matching number and the integer $k$-matching number of bipartite graphs. Thus the $MP^{k}$ number and the $SMP^{k}$ number of complete graphs, bipartite graphs and arrangement graphs are obtained, respectively. Show Chinese abstract

Abstract: 作为图的匹配预clusion数的推广，我们提供了(强)整数$k$-匹配预clusion数，简称为$MP^{k}$数($SMP^{k}$数)，这是删除后使得图既没有完美整数$k$-匹配也没有几乎完美整数$k$-匹配的边(顶点和边)的最小数目。 在本文中，我们证明当$k$为偶数时，($SMP^{k}$) $MP^{k}$ 数等于(强)分数匹配预排除数。 我们得到了具有几乎完美整数$k$-匹配的图的一个必要条件，以及二分图的匹配数与整数$k$-匹配数之间的关系表达式。 因此，分别得到了完全图、二分图和排列图的$MP^{k}$数和$SMP^{k}$数。