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Embedding longest fault-free paths in arrangement graphs with faulty vertices

The arrangement graph is a generalization of the star graph. Recent work by Hsieh et al. showed that an arrangement graph with faulty vertices contains a longest fault-free cycle. In this paper, we generalize Hsieh et al.'s result by constructing a longest fault-free path between two arbitrary distinct healthy vertices. Moreover, our result can tolerate more faulty vertices than can Hsieh et al.'s result. The situation of simultaneous faulty vertices and faulty edges is also discussed.