Short Dominating Paths and Cycles in the Binary Hypercube
نویسندگان
چکیده
A sequence of binary words of length n is called a cube dominating path, if the Hamming distance between two consecutive words is always one, and every binary word of length n is within Hamming distance one from at least one of these words. If also the first and last words are Hamming distance one apart, the sequence is called a cube dominating cycle. Bounds on the cardinality of such sequences are given, and it is shown that asymptotically the shortest cube dominating path and cycle consist of 2n(1+o(1))/n words.
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