{"paper":{"title":"First-order transducibility among classes of sparse graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.LO","authors_text":"Jakub Gajarsk\\'y, Jan Jedelsk\\'y, Jeremi G{\\l}adkowski, Micha{\\l} Pilipczuk, Szymon Toru\\'nczyk","submitted_at":"2025-05-21T15:31:33Z","abstract_excerpt":"We prove several negative results about first-order transducibility for classes of sparse graphs:\n  - for every $t \\in \\mathbb{N}$, the class of graphs of treewidth at most $t+1$ is not transducible from the class of graphs of treewidth at most $t$;\n  - for every $t \\in \\mathbb{N}$, the class of graphs with Hadwiger number at most $t+2$ is not transducible from the class of graphs with Hadwiger number at most $t$; and\n  - the class of graphs of treewidth at most $4$ is not transducible from the class of planar graphs.\n  These results are obtained by combining the known upper and lower bounds o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15655","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.15655/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"}