{"paper":{"title":"Maximizing the mean subtree order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Mol, Ortrud R. Oellermann","submitted_at":"2017-07-06T17:21:40Z","abstract_excerpt":"This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our main goal is to describe the structure of optimal trees in $\\mathcal{T}_n$ and $\\mathcal{C}_n$, the families of all trees and caterpillars, respectively, of order $n$. We begin by establishing a powerful tool called the Gluing Lemma, which is used to prove several of our main results. In particular, we show that if $T$ is an optimal tree in $\\mathcal{T}_n$ or $\\mathcal{C}_n$ for $n\\geq 4$, then every leaf of $T$ is adjacent to a vertex o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01874","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}