{"paper":{"title":"Framed 4-valent Graph Minor Theory I: Intoduction. A Planarity Criterion and Linkless Embeddability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vassily Olegovich Manturov","submitted_at":"2014-02-07T07:37:28Z","abstract_excerpt":"The present paper is the first one in the sequence of papers about a simple class of {\\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\\em minors}.\n  The goal of the whole sequence is to prove analogues of the Robertson-Seymour-Thomas theorems for framed $4$-graphs: namely, we shall prove that many minor-closed properties are classified by finitely many excluded graphs.\n  From many points of view, framed $4$-graphs are easier to consider than general graphs; on the other hand, framed $4$-graphs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1564","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"}