{"paper":{"title":"Obstructions for Minor-Closed Classes of limiting Densities Below 3/2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Antonios Kominatos, Dimitrios M. Thilikos, Reem Mahmoud","submitted_at":"2026-06-23T09:02:50Z","abstract_excerpt":"Given a graph class $\\mathcal{G}$, the limiting density of $\\mathcal{G}$ is defined as $\\delta(\\mathcal{G})=\\lim_{n\\to\\infty} \\mathsf{ex}(\\mathcal{G},n)/n$ where $\\mathsf{ex}(\\mathcal{G},n)$ is the maximum number of edges of a graph in $\\mathcal{G}$ on $n$ vertices. The limiting density $\\delta(\\mathcal{G})$ is known to be a rational number when $\\mathcal{G}$ is a minor-closed graph class. For every $\\delta\\in[0,\\frac{3}{2})$, we prove that the set of $\\subseteq$-minimal minor-closed graph classes with densities $>\\delta$ is finite and we identify it completely. A consequence of our results is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24326","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/2606.24326/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"}