{"paper":{"title":"Every graph with no $\\mathcal{K}_9^{-6}$ minor is $8$-colorable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Lafferty, Zi-Xia Song","submitted_at":"2022-09-12T14:01:23Z","abstract_excerpt":"For positive integers $t$ and $s$, let $\\mathcal{K}_t^{-s}$ denote the family of graphs obtained from the complete graph $K_t$ by removing $s$ edges. A graph $G$ has no $\\mathcal{K}_t^{-s}$ minor if it has no $H$ minor for every $H\\in \\mathcal{K}_t^{-s}$. Motivated by the famous Hadwiger's Conjecture, Jakobsen in 1971 proved that every graph with no $\\mathcal{K}_7^{-2}$ minor is $6$-colorable; very recently the present authors proved that every graph with no $\\mathcal{K}_8^{-4}$ minor is $7$-colorable. In this paper we continue our work and prove that every graph with no $\\mathcal{K}_9^{-6}$ m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.05259","kind":"arxiv","version":2},"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/2209.05259/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"}