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Embedding Hamiltonian paths in faulty arrangement graphs with the backtracking method

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2 Author(s)
Ray-Shang Lo ; Dept. of Electron. Eng., Wu Feng Inst. of Technol., Chiayi, Taiwan ; Gen-Huey Chen

The arrangement graph, denoted by An,k, is a generalization of the star graph. A recent work by S.Y. Hsieh et al. (1999) showed that when n-k⩾4 and k=2 or n-k⩾4+[k/2] and k⩾3, An,k with k(n-k)-2 random edge faults, can embed a Hamiltonian cycle. In this paper, we generalize Hsieh et al. work by embedding a Hamiltonian path between arbitrary two distinct vertices of the same An,k. To overcome the difficulty arising from random selection of the two end vertices, a new embedding method, based on a backtracking technique, is proposed. Our results can tolerate more edge faults than Hsieh et al. results as k⩾7 and 7⩽n-k⩽3+[k/2], although embedding a Hamiltonian path between arbitrary two distinct vertices is more difficult than embedding a Hamiltonian cycle

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:12 ,  Issue: 2 )