{"paper":{"title":"Graph Square Roots of Small Distance from Degree One Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Charis Papadopoulos, Paloma T. Lima, Petr A. Golovach","submitted_at":"2020-10-12T14:27:07Z","abstract_excerpt":"Given a graph class $\\mathcal{H}$, the task of the $\\mathcal{H}$-Square Root problem is to decide, whether an input graph $G$ has a square root $H$ from $\\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$ from graphs of maximum degree at most one, that is, we are looking for a square root $H$ such that there is a modulator $S$ of size $k$ such that $H-S$ is the disjoint union of isolated vertices and disjoint edges. We show that different variants of the problems with c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.05733","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/2010.05733/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"}