The fractional matching preclusion number of complete n-balanced k-partite graphs

Abstract

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 $fmp(G_{k,n})=\delta (G_{k,n})$.