Petr Gregor

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A fault-free path in the n-dimensional hypercube Qn with f faulty vertices is said to be long if it has length at least 2 n − 2f − 2. Similarly, a fault-free cycle in Qn is long if it has length at least 2 n − 2f. If all faulty vertices are from the same bipartite class of Qn, such length is the best possible. We show that for every set of at most 2n − 4(More)
In this paper, we study long cycles in induced subgraphs of hyper-cubes obtained by removing a given set of faulty vertices such that every two faults are distant. First, we show that every induced sub-graph of Q n with minimum degree n − 1 contains a cycle of length at least 2 n − 2f where f is the number of removed vertices. This length is the best(More)