Cutting resilient networks -- complete binary trees
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In our previous work, we introduced the random k-cut number for rooted graphs. In this paper, we show that the distribution of the k-cut number in complete binary trees of size n, after rescaling, is asymptotically a periodic function of n - n. Thus there are different limit distributions for different subsequences, where these limits are similar to weakly 1-stable distributions. This generalizes the result for the case k = 1, i.e., the traditional cutting model, by Janson.
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