{"paper":{"title":"Minimum-Weight Edge Discriminator in Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bhaswar B. Bhattacharya, Sayantan Das, Shirshendu Ganguly","submitted_at":"2012-10-17T08:38:49Z","abstract_excerpt":"In this paper we introduce the concept of minimum-weight edge-discriminators in hypergraphs, and study its various properties. For a hypergraph $\\mathcal H=(\\mathcal V, \\mathcal E)$, a function $\\lambda: \\mathcal V\\rightarrow \\mathbb Z^{+}\\cup\\{0\\}$ is said to be an {\\it edge-discriminator} on $\\mathcal H$ if $\\sum_{v\\in E_i}{\\lambda(v)}>0$, for all hyperedges $E_i\\in \\mathcal E$, and $\\sum_{v\\in E_i}{\\lambda(v)}\\ne \\sum_{v\\in E_j}{\\lambda(v)}$, for every two distinct hyperedges $E_i, E_j \\in \\mathcal E$. An {\\it optimal edge-discriminator} on $\\mathcal H$, to be denoted by $\\lambda_\\mathcal H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4668","kind":"arxiv","version":2},"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"}