{"paper":{"title":"Induced subgraphs and tree decompositions XIII. Basic obstructions in $\\mathcal{H}$-free graphs for finite $\\mathcal{H}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bogdan Alecu, Maria Chudnovsky, Sepehr Hajebi, Sophie Spirkl","submitted_at":"2023-11-09T00:04:35Z","abstract_excerpt":"Unlike minors, the induced subgraph obstructions to bounded treewidth come in a large variety, including, for every $t\\geq 1$, the $t$-basic obstructions: the graphs $K_{t+1}$ and $K_{t,t}$, along with the subdivisions of the $t$-by-$t$ wall and their line graphs. But this list is far from complete. The simplest example of a ''non-basic'' obstruction is due to Pohoata and Davies (independently). For every $n \\geq 1$, they construct certain graphs of treewidth $n$ and with no $3$-basic obstruction as an induced subgraph, which we call $n$-arrays. Let us say a graph class $\\mathcal{G}$ is clean "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.05066","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.05066/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"}