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It is known that $im(G) \\leq \\text{reg}(S/I(G)) \\leq m(G)$, where $\\text{reg}(S/I(G))$ is the Castelnuovo-Mumford regularity of $S/I(G)$. Cameron and Walker succeeded in classifying the finite connected simple graphs $G$ with $im(G) = m(G)$. We say that a finite connected simple graph $G$ is a Cameron-Walker graph if $im(G) = m(G)$ an"},"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":"1308.4765","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-22T05:48:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f561aad9fd0b55312249b5fbf48c6460b732ce7d47f9e8d5a41be2a77bb113d7","abstract_canon_sha256":"644ae8bcc57d82ae70bdc20d715a368058a6ef924e6838665a91212176312839"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:07.758207Z","signature_b64":"FX/OT9AsUr52l5t4uyg5JuRwo3bMNNcyFSnGuI2Ne7icRMBanV2gjQDgZwZXVCnvAFS/DUnXSYKw9wwoL9uRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aec58cb5051df845e7c1a44ebaed373a079fb328edb60d93f0e1206e91cbfa91","last_reissued_at":"2026-05-18T02:47:07.757747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:07.757747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic study on Cameron-Walker graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Akihiro Higashitani, Augustine B. O'Keefe, Kyouko Kimura, Takayuki Hibi","submitted_at":"2013-08-22T05:48:54Z","abstract_excerpt":"Let $G$ be a finite simple graph on $[n]$ and $I(G) \\subset S$ the edge ideal of $G$, where $S = K[x_{1}, \\ldots, x_{n}]$ is the polynomial ring over a field $K$. Let $m(G)$ denote the maximum size of matchings of $G$ and $im(G)$ that of induced matchings of $G$. It is known that $im(G) \\leq \\text{reg}(S/I(G)) \\leq m(G)$, where $\\text{reg}(S/I(G))$ is the Castelnuovo-Mumford regularity of $S/I(G)$. Cameron and Walker succeeded in classifying the finite connected simple graphs $G$ with $im(G) = m(G)$. 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