{"paper":{"title":"Unavoidable substructures in large and infinite $2$-edge-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Every large or infinite 2-edge-connected graph contains one of a specific list of induced subgraphs that includes chains of pinched super-clean ladders.","cross_cats":[],"primary_cat":"math.CO","authors_text":"M. N. Ellingham, Sarah Allred","submitted_at":"2025-03-27T14:53:06Z","abstract_excerpt":"In 1930, Ramsey proved that every large graph contains either a large clique or a large edgeless graph as an induced subgraph. It is well known that every large connected graph contains a long path, a large clique, or a large star as an induced subgraph. Recently Allred, Ding, and Oporowski presented the unavoidable large induced subgraphs for large and infinite $2$-connected graphs. The $2$-edge-connected (sometimes called bridgeless) graphs form an important class between connected graphs and $2$-connected graphs. In this paper we describe the unavoidable large induced subgraphs for large an"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove the existence of ubiquitous structures in 2-edge-connected graphs known as chains of pinched super-clean ladders, and incorporate these into a presentation of the unavoidable large induced subgraphs for large and infinite 2-edge-connected graphs.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The prior unavoidable-set result for 2-connected graphs (Allred, Ding, Oporowski) can be adapted to the strictly weaker 2-edge-connected setting by inserting the new ladder-chain structures without requiring additional connectivity assumptions or case distinctions that would invalidate the list.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The unavoidable large induced subgraphs of 2-edge-connected graphs are characterized via chains of pinched super-clean ladders, extending prior results for connected and 2-connected graphs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Every large or infinite 2-edge-connected graph contains one of a specific list of induced subgraphs that includes chains of pinched super-clean ladders.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"92a434dd29d7501ee5adc2d7df5a6b190924434f7447661b0763b17bd0578941"},"source":{"id":"2503.21574","kind":"arxiv","version":4},"verdict":{"id":"3806d49e-e877-43da-976d-ef1995129bf3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T22:29:07.601742Z","strongest_claim":"We prove the existence of ubiquitous structures in 2-edge-connected graphs known as chains of pinched super-clean ladders, and incorporate these into a presentation of the unavoidable large induced subgraphs for large and infinite 2-edge-connected graphs.","one_line_summary":"The unavoidable large induced subgraphs of 2-edge-connected graphs are characterized via chains of pinched super-clean ladders, extending prior results for connected and 2-connected graphs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The prior unavoidable-set result for 2-connected graphs (Allred, Ding, Oporowski) can be adapted to the strictly weaker 2-edge-connected setting by inserting the new ladder-chain structures without requiring additional connectivity assumptions or case distinctions that would invalidate the list.","pith_extraction_headline":"Every large or infinite 2-edge-connected graph contains one of a specific list of induced subgraphs that includes chains of pinched super-clean ladders."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.21574/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"}