{"paper":{"title":"Regularity and Gr\\\"obner bases of the Rees algebra of edge ideals of bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Yairon Cid-Ruiz","submitted_at":"2018-01-20T21:31:36Z","abstract_excerpt":"Let $G$ be a bipartite graph and $I=I(G)$ be its edge ideal. The aim of this note is to investigate different aspects of the Rees algebra $\\mathcal{R}(I)$ of $I$. We compute its regularity and the universal Gr\\\"obner basis of its defining equations; interestingly, both of them are described in terms of the combinatorics of $G$. We apply these ideas to study the regularity of the powers of $I$. For any $s \\ge \\text{match}(G)+\\lvert E(G) \\rvert +1$ we prove that $\\text{reg}(I^{s+1})=\\text{reg}(I^s)+2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06731","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"}