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On the discovery of the seed in uniform attachment trees
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We investigate the size of vertex confidence sets for including part of (or the entirety of) the seed in seeded uniform attachment trees, given knowledge of some of the seed's properties, and with a prescribed probability of failure. We also study the problem of identifying the leaves of a seed in a seeded uniform attachment tree, given knowledge of the positions of all internal nodes of the seed.
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Subcritical percolation and network archaeology on random recursive tree substrate networks
For random recursive trees with independent Erdős–Rényi shortcut edges, subcritical bond percolation exposes a decorated tree structure on which Jordan centrality recovers the root within a deterministic-size confidence set.
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