{"paper":{"title":"The inducibility of small oriented graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Konrad Sperfeld","submitted_at":"2011-11-21T10:30:21Z","abstract_excerpt":"We use Razborov's flag algebra method to show an asymptotic upper bound for the maximal induced density $i(\\vec P_3)$ of the orgraph $\\vec P_3$ in an arbitrary orgraph. A conjecture of Thomass\\'e states that $i(\\vec P_3)=2/5$. The hitherto best known upper bound $i(\\vec P_3)\\leq12/25$ was given by Bondy. We can show that $i(\\vec P_3)\\leq 0.4446$. Further, we consider such a maximal density for some other small orgraphs. With easy arguments one can see that $i(\\vec C_3)=1/4$, $i(\\vec K_2 \\cup \\vec E_1)=3/4$ and $2/21\\leq i(\\vec C_4)$. We show that $i(\\vec C_4)\\leq 0.1104$ and conjecture that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4813","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":""},"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"}