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We then prove that every oriented tree of order $n$ ($n\\geq 2$) with $k$ leaves is $(\\frac{3}{2}n+\\frac{3}{2}k -2)$-unavoidable and $(\\frac{9}{2}n -\\frac{5}{2}k -\\frac{9}{2})$-unavoidable, and thus $(\\frac{21}{8} n- \\frac{47}{16})$-unavoidable. Finally, we prove that every oriented tree of order $n$ with $k$ leaves is $(n+ 144k^2 - 280k + 124)$-unavoidable."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.05167","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2018-12-12T21:41:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"92e2ea5c3615c3f62af1929c34d184dfef4b0e44a68c296a41e6beae0e1bbb02","abstract_canon_sha256":"a364b7762567b3d36085846fc134af1799ecf967272e50dd78b4965d3fb04ba2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:24.295070Z","signature_b64":"tn0SRgb4F4FEX+TewCC1cOMn0asj3H6n2f7zNwQA4tDmngubgWpXS7forE/H92EOMQR6OnAZjtwr8GE2KAgCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"062780bd428ee9c7be4cdec6dfb822b0ad387a92ea36756a3a26da761d5584d6","last_reissued_at":"2026-05-17T23:58:24.294484Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:24.294484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the unavoidability of oriented trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fran\\c{c}ois Dross, Fr\\'ed\\'eric Havet","submitted_at":"2018-12-12T21:41:13Z","abstract_excerpt":"A digraph is {\\it $n$-unavoidable} if it is contained in every tournament of order $n$. We first prove that every arborescence of order $n$ with $k$ leaves is $(n+k-1)$-unavoidable. We then prove that every oriented tree of order $n$ ($n\\geq 2$) with $k$ leaves is $(\\frac{3}{2}n+\\frac{3}{2}k -2)$-unavoidable and $(\\frac{9}{2}n -\\frac{5}{2}k -\\frac{9}{2})$-unavoidable, and thus $(\\frac{21}{8} n- \\frac{47}{16})$-unavoidable. Finally, we prove that every oriented tree of order $n$ with $k$ leaves is $(n+ 144k^2 - 280k + 124)$-unavoidable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05167","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.05167","created_at":"2026-05-17T23:58:24.294587+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.05167v1","created_at":"2026-05-17T23:58:24.294587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05167","created_at":"2026-05-17T23:58:24.294587+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYTYBPKCR3U4","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYTYBPKCR3U4PPSM","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYTYBPKC","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC","json":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC.json","graph_json":"https://pith.science/api/pith-number/AYTYBPKCR3U4PPSM33DN7OBCWC/graph.json","events_json":"https://pith.science/api/pith-number/AYTYBPKCR3U4PPSM33DN7OBCWC/events.json","paper":"https://pith.science/paper/AYTYBPKC"},"agent_actions":{"view_html":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC","download_json":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC.json","view_paper":"https://pith.science/paper/AYTYBPKC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.05167&json=true","fetch_graph":"https://pith.science/api/pith-number/AYTYBPKCR3U4PPSM33DN7OBCWC/graph.json","fetch_events":"https://pith.science/api/pith-number/AYTYBPKCR3U4PPSM33DN7OBCWC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC/action/storage_attestation","attest_author":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC/action/author_attestation","sign_citation":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC/action/citation_signature","submit_replication":"https://pith.science/pith/AYTYBPKCR3U4PPSM33DN7OBCWC/action/replication_record"}},"created_at":"2026-05-17T23:58:24.294587+00:00","updated_at":"2026-05-17T23:58:24.294587+00:00"}