{"paper":{"title":"Erd\\H{o}s-P\\'osa property of rooted tree minors","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Cl\\'ement Rambaud, Eileen Robinson, Gwena\\\"el Joret, Quentin Claus","submitted_at":"2026-07-29T09:00:48Z","abstract_excerpt":"Fiorini, Joret, and Wood (2013) showed that tree minors satisfy the so-called Erd\\H{o}s-P\\'osa property with a linear bound: For every tree $T$ there exists a constant $c \\geq 1$ such that, for every graph $G$ and integer $k\\geq 0$, either $G$ contains $k$ vertex-disjoint subgraphs each containing a $T$-minor, or $G$ has a set $X$ of at most $c k$ vertices such that $G-X$ has no $T$-minor. In this paper, we prove that the same result remains true if, given a subset $S$ of vertices of $G$, one only considers $T$-minors of $G$ that are rooted in $S$. Here, a $T$-minor is rooted in $S$ if there i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26638","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/2607.26638/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"}