Limiting Probabilities for Vertices of a Given Rank in 1-2 Trees

  • Miklós Bóna
  • István Mező


We consider two varieties of labeled rooted trees, namely non-plane and plane 1-2 trees. In these tree varieties, we study the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree size goes to infinity.

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