{"paper":{"title":"Coloration of $K_7^-$-minor free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boris Albar","submitted_at":"2014-02-12T12:44:06Z","abstract_excerpt":"Hadwiger's conjecture says that every $K_t$-minor free graph is $(t - 1)$-colorable. This problem has been proved for $t \\leq 6$ but remains open for $t \\geq 7$. $K_7$-minor free graphs have been proved to be $8$-colorable (Albar & Gon\\c{c}alves, 2013). We prove here that $K_7^-$-minor free graphs are $7$-colorable, where $K_7^-$ is the graph obtained from $K_7$ by removing one edge."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2806","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":""},"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"}