Edge-fault-tolerant Hamiltonicity of pancake graphs under the conditional fault model

Authors:
Ping-Ying Tsai;Jung-Sheng Fu;Gen-Huey Chen
Affiliations:
Department of Computer Science and Information Engineering, Hwa Hsia Institute of Technology, Taipei, Taiwan, ROC;Department of Electronic Engineering, National United University, Miaoli, Taiwan, 36003, ROC;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, ROC
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

The conditional fault model imposes a constraint on the fault distribution. For example, the most commonly imposed constraint for edge faults is that each vertex is incident with two or more non-faulty edges. In this paper, subject to this constraint, we show that an n-dimensional pancake graph can tolerate up to 2n-7 edge faults, while retaining a fault-free Hamiltonian cycle, where n=4. Previously, at most n-3 edge faults can be tolerated for the same problem, if the edge faults may occur anywhere without imposing any constraint.