{"paper":{"title":"The Erd\\H{o}s-P\\'{o}sa property for circle graphs as vertex-minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J. Pascal Gollin, Meike Hatzel, O-joung Kwon, Rose McCarty, Rutger Campbell, Sang-il Oum, Sebastian Wiederrecht","submitted_at":"2025-06-04T14:02:26Z","abstract_excerpt":"We prove that for any circle graph $H$ with at least one edge and for any positive integer $k$, there exists an integer $t=t(k,H)$ so that every graph $G$ either has a vertex-minor isomorphic to the disjoint union of $k$ copies of $H$, or has a $t$-perturbation with no vertex-minor isomorphic to $H$. Using the same techniques, we also prove that for any planar multigraph $H$, every binary matroid either has a minor isomorphic to the cycle matroid of $kH$, or is a low-rank perturbation of a binary matroid with no minor isomorphic to the cycle matroid of $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03973","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/2506.03973/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"}