Embedding edge-disjoint Hamiltonian cycles in complete Josephus cubes with applications to fault-tolerant data broadcasting

Edge-disjoint Hamiltonian cycles, abbreviated as EDHCs, provide multiple edge-disjoint communication paths for data broadcasting, which greatly enhance the reliability and fault tolerance of data transmission. The complete Josephus cube $CJ{C}_n$ possesses many desirable properties as a typical interconnection network. In this paper, we focus on the construction of EDHCs in $CJ{C}_n$. We prove that there exist two EDHCs in $CJ{C}_n$ when $n\ge 3$, and three EDHCs in $CJ{C}_n$ when $n\ge 4$.