{"paper":{"title":"Graph Connectivity and Binomial Edge Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Arindam Banerjee, Luis N\\'u\\~nez-Betancourt","submitted_at":"2016-05-01T22:22:53Z","abstract_excerpt":"We relate homological properties of a binomial edge ideal $\\mathcal{J}_G$ to invariants that measure the connectivity of a simple graph $G$. Specifically, we show if $R/\\mathcal{J}_G$ is a Cohen-Macaulay ring, then graph toughness of $G$ is exactly $\\frac{1}{2}$. We also give an inequality between the depth of $R/\\mathcal{J}_G$ and the vertex-connectivity of $G$. In addition, we study the Hilbert-Samuel multiplicity, and the Hilbert-Kunz multiplicity of $R/\\mathcal{J}_G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00314","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"}