A study of large fringe and non-fringe subtrees in conditional Galton-Watson trees
Abstract
We study the conditions for families of subtrees to exist with high probability (whp) in a Galton-Walton tree of size n. We first give a Poisson approximation of fringe subtree counts, which yields the height of the maximal complete r-ary fringe subtree. Then we determine the maximal Kn such that every tree of size at most Kn appears as fringe subtree whp. Finally, we study non-fringe subtree counts and determine the height of the maximal complete r-ary non-fringe subtree.
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