{"paper":{"title":"Clique-width and induced topological minors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, the paw, or the diamond.","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Amir Nikabadi, Jadwiga Czy\\.zewska, Martin Milani\\v{c}, Pawe{\\l} Rafa{\\l} Bieli\\'nski, Pawe{\\l} Rz\\k{a}\\.zewski","submitted_at":"2026-05-14T22:35:09Z","abstract_excerpt":"A $P_4$ is a chordless path on four vertices. A diamond is a graph obtained from a clique of size four by removing one edge of the clique. A paw is a graph obtained from a clique of size four by removing two adjacent edges of the clique. We prove that for a graph $H$, the class of graphs with no induced subdivision of $H$ has bounded clique-width if and only if $H$ is an induced subgraph of $P_4$, the paw, or the diamond. This answers a~question of Dabrowski, Johnson, and Paulusma."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that for a graph H, the class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, the paw, or the diamond.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The 'only if' direction relies on the existence of explicit constructions of graphs with unbounded clique-width that still avoid induced subdivisions of any H outside the three listed graphs; this construction step is invoked in the main theorem statement (abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, paw, or diamond.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, the paw, or the diamond.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2d179f99f95bfbd997a3f9b8b0ff503838970be814fa2f8c4725ab928e1e75b0"},"source":{"id":"2605.15453","kind":"arxiv","version":1},"verdict":{"id":"dac1b27d-74b2-4202-8f20-71babc15b4d8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T14:32:44.739707Z","strongest_claim":"We prove that for a graph H, the class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, the paw, or the diamond.","one_line_summary":"The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, paw, or diamond.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The 'only if' direction relies on the existence of explicit constructions of graphs with unbounded clique-width that still avoid induced subdivisions of any H outside the three listed graphs; 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