{"paper":{"title":"Parameterized vertex deletion problems for hereditary graph classes with a block property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"D\\'aniel Marx, \\'Edouard Bonnet, Nick Brettell, O-joung Kwon","submitted_at":"2016-03-18T18:02:04Z","abstract_excerpt":"For a class of graphs $\\mathcal{P}$, the Bounded $\\mathcal{P}$-Block Vertex Deletion problem asks, given a graph $G$ on $n$ vertices and positive integers $k$ and $d$, whether there is a set $S$ of at most $k$ vertices such that each block of $G-S$ has at most $d$ vertices and is in $\\mathcal{P}$. We show that when $\\mathcal{P}$ satisfies a natural hereditary property and is recognizable in polynomial time, Bounded $\\mathcal{P}$-Block Vertex Deletion can be solved in time $2^{O(k \\log d)}n^{O(1)}$. When $\\mathcal{P}$ contains all split graphs, we show that this running time is essentially opti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05945","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":""},"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"}