Conditional fault Hamiltonicity of the complete graph

Authors:
Jung-Sheng Fu
Affiliations:
Department of Electronic Engineering, National United University, Miaoli, Taiwan
Venue:
Information Processing Letters
Year:
2008

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Abstract

Let K"n 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 K"n can tolerate up to 2n-8 edge faults, while retaining a fault-free Hamiltonian cycle, where n=4 and n@?{7,9}. When n@?{7,9},K"n contains a fault-free Hamiltonian cycle if there are up to 2n-9 edge faults. The result is optimal with respect to the number of edge faults tolerated.