Cutting Resilient Networks – Complete Binary Trees

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 (2004).