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arXiv · 1808.08140

Simply Generated Unrooted Plane Trees

Leon Ramzews·Benedikt Stufler
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Abstract

We study random unrooted plane trees with $n$ vertices sampled according to the weights corresponding to the vertex-degrees. Our main result shows that if the generating series of the weights has positive radius of convergence, then this model of random trees may be approximated geometrically by a Galton--Watson tree conditioned on having a large random size. This implies that a variety of results for the well-studied planted case also hold for unrooted trees, including Gromov--Hausdorff--Prokhorov scaling limits, tail-bounds for the diameter, distributional graph limits, and limits for the maximum degree. Our work complements results by Wang~(2016), who studied random unrooted plane trees whose diameter tends to infinity.

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Leon Ramzews, Benedikt Stufler. 2018-08-24. Simply Generated Unrooted Plane Trees. https://arxiv.org/abs/1808.08140

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