{"paper":{"title":"Packing cycles in undirected group-labelled graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Robin Thomas, Youngho Yoo","submitted_at":"2020-09-23T17:23:25Z","abstract_excerpt":"We prove a refinement of the flat wall theorem of Robertson and Seymour to undirected group-labelled graphs $(G,\\gamma)$ where $\\gamma$ assigns to each edge of an undirected graph $G$ an element of an abelian group $\\Gamma$. As a consequence, we prove that $\\Gamma$-nonzero cycles (cycles whose edges sum to a non-identity element of $\\Gamma$) satisfy the half-integral Erd\\H{o}s-P\\'osa property, and we also recover a result of Wollan that, if $\\Gamma$ has no element of order two, then $\\Gamma$-nonzero cycles satisfy the Erd\\H{o}s-P\\'osa property. As another application, we prove that if $m$ is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11266","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/2009.11266/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"}