{"paper":{"title":"The Minimal Automorphism-Free Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ilhee Kim, Paul Seymour, Ringi Kim","submitted_at":"2013-03-06T21:23:56Z","abstract_excerpt":"A finite tree $T$ with $|V(T)| \\geq 2$ is called {\\it automorphism-free} if there is no non-trivial automorphism of $T$. Let $\\mathcal{AFT}$ be the poset with the element set of all finite automorphism-free trees (up to graph isomorphism) ordered by $T_1 \\preceq T_2$ if $T_1$ can be obtained from $T_2$ by successively deleting one leaf at a time in such a way that each intermediate tree is also automorphism-free. In this paper, we prove that $\\mathcal{AFT}$ has a unique minimal element. This result gives an affirmative answer to the question asked by Rupinski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1551","kind":"arxiv","version":1},"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"}