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Component sizes in the supercritical percolation on the binary cube
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We present a relatively short and self-contained proof of the classical result on component sizes in the supercritical percolation on the high dimensional binary cube, due to Ajtai, Koml\'os and Szemer\'edi (1982) and to Bollob\'as, Kohayakawa and \L uczak (1992).
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Cited by 2 Pith papers
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Nearly spanning cycle in the percolated hypercube
For every epsilon > 0 there is a C such that the percolated hypercube Q_d^p with p >= C/d contains, with high probability, a cycle of length at least (1-epsilon)2^d.
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Cycle lengths in the percolated hypercube
With high probability, the percolated hypercube Q^d_{c/d} contains cycles of every even length between 4 and (1-epsilon)2^d.
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