Conditional edge-fault-tolerant Hamiltonicity of the data center network

The k-dimensional data center network with n port switches, denoted by Dk,n, has been proposed for data centers as a server centric network structure. Wang et al. (2015) had shown that Dk,n is (n+k−3)-fault-tolerant Hamiltonian. In this paper, we consider more faulty edges and prove that Dk,n is conditional (2n+2k−9)-edge-fault-tolerant Hamiltonian for any k≥0 and n≥2 except k=1 and n≥6. Moreover, the upper bound 2n+2k−9 of |F| is optimal.