{"paper":{"title":"Giant descendant trees, matchings and independent sets in the age-biased attachment graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Frieze, Boris Pittel, Huseyin Acan","submitted_at":"2019-08-07T00:24:15Z","abstract_excerpt":"We study two models of an age-biased graph process: the $\\delta$-version of the preferential attachment graph model (PAM) and the uniform attachment graph model (UAM), with $m$ attachments for each of incoming vertices. We show that almost surely the scaled size of a breadth-first (descendant) tree rooted at a fixed vertex converges, for $m=1$, to a limit whose distribution is a mixture of two beta-distributions and a single beta-distribution respectively, and that for $m>1$ the limit is $1$. We also analyze the likely performance of two greedy (online) algorithms, for a large matching set and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02407","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02407/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}