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).
@article{10_37236_8350,
author = {Xing Shi Cai and Cecilia Holmgren},
title = {Cutting resilient networks -- complete binary trees},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8350},
zbl = {1427.60017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8350/}
}
TY - JOUR
AU - Xing Shi Cai
AU - Cecilia Holmgren
TI - Cutting resilient networks -- complete binary trees
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8350/
DO - 10.37236/8350
ID - 10_37236_8350
ER -
%0 Journal Article
%A Xing Shi Cai
%A Cecilia Holmgren
%T Cutting resilient networks -- complete binary trees
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8350/
%R 10.37236/8350
%F 10_37236_8350
Xing Shi Cai; Cecilia Holmgren. Cutting resilient networks -- complete binary trees. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8350
