Long paths and cycles in faulty hypercubes: existence, optimality, complexity
نویسندگان
چکیده
A fault-free cycle in the n-dimensional hypercube Qn with f faulty vertices is long if it has length at least 2 − 2f . If all faulty vertices are from the same bipartite class of Qn, such length is the best possible. We prove a conjecture of Castañeda and Gotchev [2] asserting that fn = ( n 2 ) −2 where fn is the largest integer such that for every set of at most fn faulty vertices, there exists a long fault-free cycle in Qn. Furthermore, we present several results on similar problems of long paths and long routings in faulty hypercubes and their complexity.
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عنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 34 شماره
صفحات -
تاریخ انتشار 2009