{"paper":{"title":"A Sublinear Tester for Outerplanarity (and Other Forbidden Minors) With One-Sided Error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hendrik Fichtenberger, Maximilian W\\\"otzel, Reut Levi, Yadu Vasudev","submitted_at":"2017-07-19T14:44:55Z","abstract_excerpt":"We consider one-sided error property testing of $\\mathcal{F}$-minor freeness in bounded-degree graphs for any finite family of graphs $\\mathcal{F}$ that contains a minor of $K_{2,k}$, the $k$-circus graph, or the $(k\\times 2)$-grid for any $k\\in\\mathbb{N}$. This includes, for instance, testing whether a graph is outerplanar or a cactus graph. The query complexity of our algorithm in terms of the number of vertices in the graph, $n$, is $\\tilde{O}(n^{2/3} / \\epsilon^5)$. Czumaj et~al.\\ showed that cycle-freeness and $C_k$-minor freeness can be tested with query complexity $\\tilde{O}(\\sqrt{n})$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06126","kind":"arxiv","version":4},"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"}