{"paper":{"title":"Forbidding anticomplete planar minors: Induced Erd\\H{o}s--P\\'osa property and Maximum Independent Set in QP","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amadeus Reinald, Maria Chudnovsky, St\\'ephan Thomass\\'e","submitted_at":"2026-07-10T17:43:39Z","abstract_excerpt":"The Erd\\H{o}s--P\\'osa theorem asserts that every graph $G$ with no $k$ disjoint cycles contains a set $X$ of $f(k)$ vertices such that $G\\setminus X$ has no cycle. Robertson and Seymour showed that this Erd\\H{o}s--P\\'osa property also holds for $H$-minor models of any planar graph $H$. Equivalently, if $G$ has no $k$ minor models of $H$ pairwise at distance at least 1 (i.e. disjoint), then one can remove $f(k,H)$ balls of radius 0 (i.e. vertices) to make the graph $H$-minor free.\n  We show that this coarse graph theory point of view generalizes to distance at least 2 versus radius 1 balls, yie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09646","kind":"arxiv","version":1},"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/2607.09646/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"}