{"paper":{"title":"An edge variant of the Erd\\H{o}s-P\\'osa property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Dimitrios M. Thilikos, Ignasi Sau, Jean-Florent Raymond","submitted_at":"2013-11-05T16:13:28Z","abstract_excerpt":"For every $r\\in \\mathbb{N}$, we denote by $\\theta_{r}$ the multigraph with two vertices and $r$ parallel edges. Given a graph $G$, we say that a subgraph $H$ of $G$ is a model of $\\theta_{r}$ in $G$ if $H$ contains $\\theta_{r}$ as a contraction. We prove that the following edge variant of the Erd{\\H o}s-P{\\'o}sa property holds for every $r\\geq 2$: if $G$ is a graph and $k$ is a positive integer, then either $G$ contains a packing of $k$ mutually edge-disjoint models of $\\theta_{r}$, or it contains a set $S$ of $f_r(k)$ edges such that $G\\setminus S$ has no $\\theta_{r}$-model, for both $f_r(k) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1108","kind":"arxiv","version":3},"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"}