{"paper":{"title":"The hardness of the independence and matching clutter of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Hovhannes Sargsyan, Sasun Hambardzumyan, Vahan V. Mkrtchyan, Vahe L. Musoyan","submitted_at":"2009-03-28T02:15:17Z","abstract_excerpt":"A {\\it clutter} (or {\\it antichain} or {\\it Sperner family}) $L$ is a pair $(V,E)$, where $V$ is a finite set and $E$ is a family of subsets of $V$ none of which is a subset of another. Usually, the elements of $V$ are called {\\it vertices} of $L$, and the elements of $E$ are called {\\it edges} of $L$. A subset $s_e$ of an edge $e$ of a clutter is called {\\it recognizing} for $e$, if $s_e$ is not a subset of another edge. The {\\it hardness} of an edge $e$ of a clutter is the ratio of the size of $e\\textrm{'s}$ smallest recognizing subset to the size of $e$. The hardness of a clutter is the max"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4907","kind":"arxiv","version":4},"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"}