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The Betti numbers only depend on the multiset of the number of neighbors in $S$ the $x_i$'s have. Singh and Verma have earlier determined the Betti numbers for complete split graphs (where all $y_i$ are neighbors to all $x_j$), and for \"nearly complete\" split graphs (where al"},"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":"2606.03101","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AC","submitted_at":"2026-06-02T03:39:24Z","cross_cats_sorted":[],"title_canon_sha256":"94ee575718857cf79832353c837c71e9f471323da9d0b16b95656b10986a2938","abstract_canon_sha256":"ebe90bf0a9b40c1dce198bd6c5dc31e56374ffc48b5bb7ef6ac410d02e3ba290"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:31.703065Z","signature_b64":"VfXIprCJDNGppK63e0jktj5xSQ7d4pFT7I/ayefVv/9jFv9VXEJPV5SLAB1r9GY6NalVlghGk9LtV0u2LdHaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cca29123731c32d389a6707ff68e62167b3b73d2b9892d4954106699adb1f89f","last_reissued_at":"2026-06-03T01:05:31.702700Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:31.702700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Betti numbers of split graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ralf Fr\\\"oberg","submitted_at":"2026-06-02T03:39:24Z","abstract_excerpt":"A split graph is a graph where the vertices are a disjoint union of a complete part $C=\\{x_i,\\ldots,x_n\\}$ and a stable part $S=\\{y_1,\\ldots,y_m\\}$. 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