{"paper":{"title":"Supercritical Size-Width Tree-Like Resolution Trade-Offs for Graph Isomorphism","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.LO","authors_text":"Christoph Berkholz, Harry Vinall-Smeeth, Moritz Lichter","submitted_at":"2024-07-25T11:07:28Z","abstract_excerpt":"We study the refutation complexity of graph isomorphism in the tree-like resolution calculus. Tor\\'an and W\\\"orz (TOCL 2023) showed that there is a resolution refutation of narrow width $k$ for two graphs if and only if they can be distinguished in ($k+1$)-variable first-order logic (FO$^{k+1}$) and hence by a count-free variant of the $k$-dimensional Weisfeiler-Leman algorithm. While DAG-like narrow width $k$ resolution refutations have size at most $n^k$, tree-like refutations may be much larger. We show that there are graphs of order n, whose isomorphism can be refuted in narrow width $k$ b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17947","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.17947/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}