… reliability to the study of percolation on trees. To a complete k-ary tree Tk,n of depth n we …
In section 3 we apply this method to study percolation on complete trees. This is a new and …

… We consider supercritical Bernoulli bond percolation on a large b-ary tree, in the sense
that with high probability, there exists a giant cluster. We show that the size of the giant cluster …

… Then, we have a finite k-ary tree with probability one if 0 ≤ p ≤ 1/k. Moreover, we give
the expectation and variance of the length of ideal codewords for representing the finite …

… sharp for odd length paths, and for k > 2 his lower bound is sharp for complete k-ary trees
and complete k − 1-ary trees. Note, this is precisely the cases of Theorem 3.8 with k = N,N + 1. …

… k-ary trees of order n. Zaks (1980) gave the following representation of k-ary trees. Let T be
… to left in a row by the inner loop, where the percolation is made by Eq. (3.4). After this step, …

… : if the branching number of a tree is strictly smaller than k, then the critical probability is 1,
while it is 1 − 1/k on the k-ary tree. A related result is that in any rooted tree T there is a way of …

… k-ary trees of order n. Zaks [18] gave the following representation of k-ary trees. Let T be a …
right to left in a row by the inner loop, where the percolation is made by Eq. (3.4). After this step…

… Figure 7: The percolation function of binary tree 3.2 Percolation on k-ary Trees Now we
extend the percolation process from a binary tree to a k-ary tree. Similar to the binary …

Percolation on a k-ary Tree … Percolation on a k-ary Tree …

… percolation under tunable limited knowledge influences the giant component P∞, the critical
threshold pc, and derive analytical relations for the percolation … , where a k-ary tree admits, …