The fractional matching preclusion number of a graph G, denoted by fmp(G), is the minimum number of edges whose deletion results in a graph with no fractional perfect matchings. Let \(G_{k,n}\) be the complete n-balanced k-partite graph, whose vertex set can be partitioned into k parts, each has n vertices and whose edge set contains all edges between two distinct parts. In this paper, we prove that if \(k=3\) or 5 and \(n=1\), then \(fmp(G_{k,n})=\delta (G_{k,n})-1\); otherwise \(fmp(G_{k,n})=\delta (G_{k,n})\).

中文翻译：

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完全n-平衡k-部图的分数匹配排除数

图G的分数匹配排除数，用fmp ( G ) 表示，是其删除导致图没有分数完美匹配的最小边数。令\(G_{k,n}\)是完整的n平衡k部分图，其顶点集可以划分为k个部分，每个部分有n个顶点，其边集包含两个不同部分之间的所有边。在本文中，我们证明如果\(k=3\)或 5 且\(n=1\)，则\(fmp(G_{k,n})=\delta (G_{k,n})- 1\) ; 否则\(fmp(G_{k,n})=\delta (G_{k,n})\).