The fractional (strong) matching preclusion number of complete k-partite graph

Abstract

The fractional (strong) matching preclusion number of a graph G, denoted by f(s)mp(G), is the minimum number of edges (and vertices) whose deletion results in a graph with no fractional perfect matching. Let Gn1,n2,…,nk be the complete k-partite graph, whose vertex set can be partitioned into k parts, each has ni(1≤i≤k) vertices and whose edge set contains all edges between two distinct parts. In this paper, we determine fmp(Gn1,n2,…,nk) and fsmp(Gn1,n2,…,nk).