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Fault-tolerant Hamiltonicity in a class of faulty meshes

Fault-tolerant Hamiltonicity in a class of faulty meshes,10.1016/j.amc.2006.06.009,Applied Mathematics and Computation,Xiaofan Yang,Jun Luo,Shuangqing

Fault-tolerant Hamiltonicity in a class of faulty meshes   (Citations: 2)
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This paper addresses the Hamiltonian properties of rectangular meshes with faulty nodes. We present a necessary and sufficient condition for an m×n mesh (m⩾4 and n⩾4 are even) with two faulty nodes to have a fault-free Hamiltonian cycle, which generalizes a result owing to Kim and Yoon [J.S. Kim, S.H. Yoon, Embedding of rings in 2-D meshes and tori with faulty nodes, Journal of Systems Architecture 43 (9) (1997) 643–654]. We also describe an efficient scheme for constructing such a fault-free Hamiltonian cycle, if there is.
Journal: Applied Mathematics and Computation - AMC , vol. 182, no. 2, pp. 1696-1708, 2006
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