{"paper":{"title":"Graph properties in node-query setting: effect of breaking symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"Nikhil Balaji, Raghav Kulkarni, Samir Datta, Supartha Podder","submitted_at":"2015-10-28T11:47:33Z","abstract_excerpt":"The query complexity of graph properties is well-studied when queries are on edges. We investigate the same when queries are on nodes. In this setting a graph $G = (V, E)$ on $n$ vertices and a property $\\mathcal{P}$ are given. A black-box access to an unknown subset $S \\subseteq V$ is provided via queries of the form `Does $i \\in S$?'. We are interested in the minimum number of queries needed in worst case in order to determine whether $G[S]$, the subgraph of $G$ induced on $S$, satisfies $\\mathcal{P}$.\n  Apart from being combinatorially rich, this setting allows us to initiate a systematic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08267","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"}