The　k-ary　n-cube　Qnk　serves　as　an　indispensable　interconnection　network　in　the　design　of　data　center　networks,　network-on-chips,　and　parallel　computing　systems　since　it　possesses　numerous　attractive　properties.　In　these　parallel　architectures,　the　paired　(or　unpaired)　many-to-many　m-disjoint　path　cover　(m-DPC)　plays　a　significant　role　in　message　transmission.　Nevertheless,　the　construction　of　m-DPC　is　severely　obstructed　by　large-scale　edge　faults　due　to　the　rapid　growth　of　the　system　scale.　In　this　paper,　we　investigate　the　existence　of　paired　2-DPC　in　Qnk　under　the　partitioned　edge　fault　(PEF)　model,　which　is　a　novel　fault　model　for　enhancing　the　networks＇　fault-tolerance　related　to　path　embedding　problem.　We　exploit　this　model　to　evaluate　the　edge　fault-tolerance　of　Qnk　when　a　paired　2-DPC　is　embedded　into　Qnk.　Compared　to　the　other　known　works,　our　results　can　help　Qnk　to　achieve　large-scale　edge　fault-tolerance.　©　2024　Elsevier　Inc.