{"paper":{"title":"A unified Erd\\H{o}s-P\\'osa theorem for constrained cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Joos, Paul Wollan, Tony Huynh","submitted_at":"2016-05-23T16:34:10Z","abstract_excerpt":"A doubly group-labeled graph is an oriented graph with its edges labeled by elements of the direct sum of two groups $\\Gamma_1,\\Gamma_2$. A cycle in a doubly group-labeled graph is $(\\Gamma_1,\\Gamma_2)$-non-zero if it is non-zero in both coordinates. Our main result is a generalization of the Flat Wall Theorem of Robertson and Seymour to doubly group-labeled graphs. As an application, we determine all canonical obstructions to the Erd\\H{o}s-P\\'osa property for $(\\Gamma_1,\\Gamma_2)$-non-zero cycles in doubly group-labeled graphs. The obstructions imply that the half-integral Erd\\H{o}s-P\\'osa pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07082","kind":"arxiv","version":5},"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"}