{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CANCY4OUGLHZV24HYQCEOSAAIU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3cd2a119a719ebfe624284e12ca337f867b22946042ebfff64453b63dba930da","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-07-22T16:57:16Z","title_canon_sha256":"3dda63d3df198d2123410fd25a70ba75c669cfa7ffd40e74481730b966663d0b"},"schema_version":"1.0","source":{"id":"1507.06254","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06254","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06254v2","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06254","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"CANCY4OUGLHZ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CANCY4OUGLHZV24H","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CANCY4OU","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:b1917d80e6f7e231e9ae6d4baff37fb35df09138ccd17787384f6d64540daab6","target":"graph","created_at":"2026-05-18T00:53:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $G$ be a distance-regular graph of order $v$ and size $e$. In this paper, we show that the max-cut in $G$ is at most $e(1-1/g)$, where $g$ is the odd girth of $G$. This result implies that the independence number of $G$ is at most $\\frac{v}{2}(1-1/g)$. We use this fact to also study the extendability of matchings in distance-regular graphs. A graph $G$ of even order $v$ is called $t$-extendable if it contains a perfect matching, $t<v/2$ and any matching of $t$ edges is contained in some perfect matching. The extendability of $G$ is the maximum $t$ such that $G$ is $t$-extendable. We genera","authors_text":"Jack H. Koolen, Sebastian M. Cioab\\u{a}, Weiqiang Li","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-07-22T16:57:16Z","title":"Max-cut and extendability of matchings in distance-regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06254","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:21df30223b6058e4e2963f067db7b7b99f091ee7f535a3377324039971776995","target":"record","created_at":"2026-05-18T00:53:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3cd2a119a719ebfe624284e12ca337f867b22946042ebfff64453b63dba930da","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-07-22T16:57:16Z","title_canon_sha256":"3dda63d3df198d2123410fd25a70ba75c669cfa7ffd40e74481730b966663d0b"},"schema_version":"1.0","source":{"id":"1507.06254","kind":"arxiv","version":2}},"canonical_sha256":"101a2c71d432cf9aeb87c404474800452d2481a78585334190bc9bb4a5bb127b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"101a2c71d432cf9aeb87c404474800452d2481a78585334190bc9bb4a5bb127b","first_computed_at":"2026-05-18T00:53:17.798878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:17.798878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eIlVkZScTSrHGDLnBilFZrcjovt2n4N2ijvO3S8TwSK1qGayxb0/KFj1QAzZUfImyJr2gWifZZanlk+FtypgDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:17.799344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06254","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21df30223b6058e4e2963f067db7b7b99f091ee7f535a3377324039971776995","sha256:b1917d80e6f7e231e9ae6d4baff37fb35df09138ccd17787384f6d64540daab6"],"state_sha256":"730edab55fae73bb35456f6720388e4eb920f7fd152716c30b6b6c001b784edc"}