Conditional fault Hamiltonicity of the complete graph

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Abstract

Let Kn denote a complete graph of n nodes. In this paper, assuming that each vertex is incident with at least two fault-free links, we show that Kn can tolerate up to 2n8 edge faults, while retaining a fault-free Hamiltonian cycle, where n4 and n{7,9}. When n{7,9},Kn contains a fault-free Hamiltonian cycle if there are up to 2n9 edge faults. The result is optimal with respect to the number of edge faults tolerated.

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    Citation Excerpt :

    With the inspiration of the work by Fu [7] in the study of 2-conditional edge-fault tolerant hamiltonicity of the complete graph, Ho et al. [12] begin the study on 3-conditional edge-fault tolerant hamiltonian connectivity of the complete graph.

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