{"paper":{"title":"A short derivation of the structure theorem for graphs with excluded topological minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Wei{\\ss}auer, Joshua Erde","submitted_at":"2018-07-03T12:31:58Z","abstract_excerpt":"As a major step in their proof of Wagner's conjecture, Robertson and Seymour showed that every graph not containing a fixed graph $H$ as a minor has a tree-decomposition in which each torso is almost embeddable in a surface of bounded genus. Recently, Grohe and Marx proved a similar result for graphs not containing $H$ as a topological minor. They showed that every graph which does not contain $H$ as a topological minor has a tree-decomposition in which every torso is either almost embeddable in a surface of bounded genus, or has a bounded number of vertices of high degree. We give a short pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01119","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"}