Abstract : An example is given which shows that, in general, conditioned Galton-Watson trees cannot be obtained by adding vertices one by one, while this can be done in some important but special cases, as shown by Luczak and Winkler.
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Svante Janson. Conditioned Galton-Watson trees do not grow. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.331-334, ⟨10.46298/dmtcs.3483⟩. ⟨hal-01184685⟩