Embedding the n-cube in lower dimensions
P Frankl, H Maehara - European Journal of Combinatorics, 1986 - Elsevier
P Frankl, H Maehara
European Journal of Combinatorics, 1986•ElsevierLet m= m (n) denote the smallest dimension m such that the vertices of the n-dimensional
cube can be embedded into E m in a way that adjacent vertices have distance at most 1
while any two non-adjacent vertices are at distance more than 1. It is proved that (1+ o (1))
n/log 2 n< m (n)<(2log 2 3+ o (1)) n/log 2 n holds.
cube can be embedded into E m in a way that adjacent vertices have distance at most 1
while any two non-adjacent vertices are at distance more than 1. It is proved that (1+ o (1))
n/log 2 n< m (n)<(2log 2 3+ o (1)) n/log 2 n holds.
Let m = m (n) denote the smallest dimension m such that the vertices of the n-dimensional cube can be embedded into Em in a way that adjacent vertices have distance at most 1 while any two non-adjacent vertices are at distance more than 1. It is proved that (1 + o(1))n/log2n < m (n) < (2log23+o(1))n/log2n holds.
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