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 ) m p ( G ) , is the minimum number of edges (and vertices) whose deletion results in a graph with no fractional perfect matching. Let G n 1 , n 2 , … , n k be the complete k-partite graph, whose vertex set can be partitioned into k parts, each has n i ( 1 ≤ i ≤ k ) vertices and whose edge set contains all edges between two distinct parts. In this paper, we determine f m p ( G n 1 , n 2 , … , n k ) and f s m p ( G n 1 , n 2 , … , n k ) .