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Lecture Notes in Computer Science
We investigate hamiltonian properties of Pm × Cn, m ≥ 2 and even n ≥ 4, which is bipartite, in the presence of faulty vertices and/or edges. We show that Pm×Cn with n even is strongly hamiltonianlaceable if the number of faulty elements is one or less. When the number of faulty elements is two, it has a fault-free cycle of length at least mn−2 unless both faulty elements are contained in the same partite vertex set; otherwise, it has a fault-free cycle of length mn−4. A sufficient condition isdoi:10.1007/3-540-45071-8_33 fatcat:jufyle6fkvecfhy63xfl3bjktu