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arXiv · 1811.05673

Cutting resilient networks -- complete binary trees

Xing Shi Cai·Cecilia Holmgren
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Abstract

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 $\lg n - \lg \lg n$. 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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Xing Shi Cai, Cecilia Holmgren. 2019-11-11. Cutting resilient networks -- complete binary trees. https://doi.org/10.37236/8350

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