Percolation on a k-Ary Tree

  • K. Kobayashi
  • H. Morita
  • M. Hoshi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)


Starting from the root, extend k branches and append k children with probability p, or terminate with probability q=1–p. 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 trees. Furthermore, we establish the probability of obtaining infinite tree, that is, of penetrating to infinity without termination for case 1/kp ≤1.


Binary Tree Internal Node IEEE International Symposium Percolation Model Catalan Number 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • K. Kobayashi
  • H. Morita
  • M. Hoshi

There are no affiliations available

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