{"paper":{"title":"The Descriptive Complexity of Subgraph Isomorphism without Numerics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Maksim Zhukovskii, Oleg Verbitsky","submitted_at":"2016-07-27T12:53:57Z","abstract_excerpt":"Let $F$ be a connected graph with $\\ell$ vertices. The existence of a subgraph isomorphic to $F$ can be defined in first-order logic with quantifier depth no better than $\\ell$, simply because no first-order formula of smaller quantifier depth can distinguish between the complete graphs $K_\\ell$ and $K_{\\ell-1}$. We show that, for some $F$, the existence of an $F$ subgraph in \\emph{sufficiently large} connected graphs is definable with quantifier depth $\\ell-3$. On the other hand, this is never possible with quantifier depth better than $\\ell/2$. If we, however, consider definitions over conne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08067","kind":"arxiv","version":4},"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"}