The　Hamiltonian　path/cycle　serves　as　a　robust　tool　for　transmitting　messages　within　parallel　and　distributed　systems.　However,　the　prevalent　device　-intensive　nature　of　these　systems　often　leads　to　the　occurrence　of　faults.　Tackling　the　critical　challenge　of　tolerating　numerous　faults　when　constructing　Hamiltonian　paths　and　cycles　in　these　systems　is　of　utmost　significance.　The　alternating　group　graph　AG　n　is　a　suitable　interconnection　network　for　building　parallel　and　distributed　systems　due　to　its　outstanding　topological　properties.　Many　studies　have　been　dedicated　to　the　fault　-tolerant　embedding　of　Hamiltonian　paths　and　cycles　in　AG　n　,　but　they　all　fail　to　reach　the　desired　level　of　fault　-tolerance.　In　this　paper,　we　aim　to　enhance　the　edge　fault　-tolerant　embedding　capability　of　AG　n　by　leveraging　a　newly　emerged　fault　model,　called　the　Partitioned　Edge　Fault　(PEF)　model.　We　prove　the　existence　of　Hamiltonian　paths/cycles　tolerating　large-scale　edge　faults　in　AG　n　under　the　PEF　model.　Additionally,　we　propose　a　fault　-tolerant　Hamiltonian　path　embedding　algorithm　for　AG　n　under　the　PEF　model　and　validate　its　effectiveness　through　experiments.　To　gauge　the　significance　of　each　missed　edge,　we　conduct　experimental　calculations　for　the　average　path　length　of　every　edge　along　the　Hamiltonian　path　produced　by　the　proposed　embedding　algorithm.　Furthermore,　the　fault　-tolerance　comparison　and　experimental　analysis　reveal　that　our　results　improve　the　fault　-tolerant　embedding　capability　of　AG　n　from　a　linear　level　to　an　exponential　one.　To　our　knowledge,　this　is　the　first　time　that　a　Hamiltonian　path/cycle　embedding　approach　is　proposed　and　actually　implemented　for　AG　n　with　large-scale　edge　faults.