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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 $\\text{reg}(I^{s+1})=\\text{reg}(I^s)+2$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1801.06731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-20T21:31:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"34d16a66a79250f16443520173decc41f165ae6b333d4799d02bc92036fc8ca9","abstract_canon_sha256":"b37d570e25807c66bee3f3db863f04b74600441bade2b79880909c43bb068b38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:21.267120Z","signature_b64":"pL1rJ1lKpcqqS3CbjBxWnV2SJmRnvKpnZtREQp0bUkob2zI8a+M1ohgskZdPYU6nXwXcHOeKHHjVVVbXbRHaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4d0d49de9f7a5ae813979bf2ac125bc2c78a684d7f08b957d87484969072eba","last_reissued_at":"2026-05-18T00:16:21.266741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:21.266741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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