{"paper":{"title":"An $O(\\log OPT)$-approximation for covering and packing minor models of ${\\theta}_r$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Dimitrios M. Thilikos, Dimitris Chatzidimitriou, Ignasi Sau, Jean-Florent Raymond","submitted_at":"2015-10-14T01:41:15Z","abstract_excerpt":"Given two graphs $G$ and $H$, we define $\\textsf{v-cover}_{H}(G)$ (resp. $\\textsf{e-cover}_{H}(G)$) as the minimum number of vertices (resp. edges) whose removal from $G$ produces a graph without any minor isomorphic to ${H}$. Also $\\textsf{v-pack}_{H}(G)$ (resp. $\\textsf{v-pack}_{H}(G)$) is the maximum number of vertex- (resp. edge-) disjoint subgraphs of $G$ that contain a minor isomaorphic to $H$. We denote by $\\theta_r$ the graph with two vertices and $r$ parallel edges between them. When $H=\\theta_r$, the parameters $\\textsf{v-cover}_{H}$, $\\textsf{e-cover}_{H}$, $\\textsf{v-pack}_{H}$, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03945","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":""},"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"}