BCube　stands　as　a　renowned　server-centric　data　center　network　(DCN),　boasting　numerous　advantages,　such　as　low　diameter,　high　aggregate　throughput,　and　abundant　parallel　paths.　As　DCNs　expand　rapidly,　followed　by　the　daily　increasing　likelihood　of　failures,　fault　tolerance　has　become　an　important　issue　in　DCNs.　Hamiltonian　paths　constitute　a　pivotal　network　topology　for　parallel　and　distributed　computing,　suitable　for　designing　deadlock-free　routing　algorithms,　fault-tolerant　routing　algorithms,　and　congestion　avoidance.　The　partitioned　edge　fault　(PEF)　model　is　a　recently　proposed　fault　model　that　exploits　the　properties　of　networks　to　achieve　fault　tolerance　with　an　exponential　scale.　In　this　paper,　we　explore　the　existence　of　Hamiltonian　paths　in　BCube　under　the　PEF　model.　Since　one　switch　failure　will　result　in　multiple　faulty　links,　we　also　extend　the　conclusions　related　to　Hamiltonian　paths　to　analyze　the　fault　tolerance　of　BCube　under　the　PEF　model　when　switch　failures　occur.　Moreover,　we　provide　algorithms　to　embed　a　Hamiltonian　path　between　arbitrary　two　distinct　servers　into　BCube　under　the　PEF　model.　Experimental　analysis　and　comparisons　demonstrate　that　our　approach　exhibits　exponential　enhancements　over　the　other　known　results,　and　BCube　DCNs　possess　remarkable　fault　tolerance　in　response　to　both　link　and　switch　failures　under　the　PEF　model.　As　a　by-product,　we　obtain　a　deadlock-free　routing　based　on　the　constructed　Hamiltonian　path　and　assess　the　routing　performance　compared　to　the　benchmark　routing　algorithms.　©　2004-2012　IEEE.