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- W2224559739 abstract "We study the connectivity of random subgraphs of the $d$-dimensional Hamming graph $H(d, n)$, which is the Cartesian product of $d$ complete graphs on $n$ vertices. We sample the random subgraph with an i.i.d. Bernoulli bond percolation on $H(d,n)$ with parameter $p$. We identify the window of the transition: when $ np- log n to - infty $ the probability that the graph is connected tends to $0$, while when $ np- log n to + infty $ it converges to $1$. We also investigate the connectivity probability inside the critical window, namely when $ np- log n to t in mathbb{R} $. We find that the threshold does not depend on $d$, unlike the phase transition of the giant connected component of the Hamming graph (see [1]). Within the critical window, the connectivity probability does depend on $d$. We determine how." @default.
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- W2224559739 date "2016-01-01" @default.
- W2224559739 modified "2023-09-25" @default.
- W2224559739 title "Connectivity threshold for random subgraphs of the Hamming graph" @default.
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- W2224559739 doi "https://doi.org/10.1214/16-ecp4479" @default.
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