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Component sizes in the supercritical percolation on the binary cube

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arxiv 2311.07210 v1 pith:K34MD26L submitted 2023-11-13 math.CO math.PR

classification math.COmath.PR
keywords binarycomponentcubepercolationsizessupercriticalajtaibollob
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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

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nearly spanning cycle in the percolated hypercube

    math.CO 2025-05 conditional novelty 8.0 of 10

    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.

  2. Cycle lengths in the percolated hypercube

    math.CO 2025-06 conditional novelty 7.0 of 10

    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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