As a generalization of matching preclusion number of a graph, we provide the (strong) integer k-matching preclusion number, abbreviated as MPᵏ number (SMPᵏ 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 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. And then the MPᵏ number and the SMPᵏ number of complete graphs, bipartite graphs and arrangement graphs are obtained, respectively.
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Chang et al. (2024) studied this question.
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