{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DMXQ7ZAU3B6MOV7Q6R5BD6FGP4","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":"f16fbc7375fa0567916b69b19886056d17901b3078b4b58ecfbb2efb2c879692","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2018-10-03T16:31:24Z","title_canon_sha256":"5a8852caf9773e086c8fcc6327adcb6b62072038e66f71d543ad4143abcaace5"},"schema_version":"1.0","source":{"id":"1810.01832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01832","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01832v2","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01832","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"DMXQ7ZAU3B6M","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMXQ7ZAU3B6MOV7Q","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMXQ7ZAU","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:41b77d6cb985dcc640867ce2fdcca576e4dbfb0a43f1ac605563e72c49d2f6d8","target":"graph","created_at":"2026-05-18T00:04:07Z","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":"Consider a graph with $n$ vertices where the shortest odd cycle is of length $>2k+1$. We revisit two known results about such graphs:\n  (I) Such a graph is almost bipartite, in the sense that it can be made bipartite by removing from it $O\\bigl( (n/k) \\log (n/k) \\bigr)$ vertices. While this result is known [GKL97] -- our new proof seems to yield slightly better constants, and is (arguably) conceptually simpler. To this end, we state (and prove) a version of CKR partitions [CKR01, FRT04] that has a small vertex separator, and it might be of independent interest. While this must be known in the ","authors_text":"Saladi Rahul, Sariel Har-Peled","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2018-10-03T16:31:24Z","title":"Two (Known) Results About Graphs with No Short Odd Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01832","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:c748cfb66bbf268df724d37a98ea53f2c171fbdaa6cd2a2c7c50f3fe7ee6b0d4","target":"record","created_at":"2026-05-18T00:04:07Z","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":"f16fbc7375fa0567916b69b19886056d17901b3078b4b58ecfbb2efb2c879692","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2018-10-03T16:31:24Z","title_canon_sha256":"5a8852caf9773e086c8fcc6327adcb6b62072038e66f71d543ad4143abcaace5"},"schema_version":"1.0","source":{"id":"1810.01832","kind":"arxiv","version":2}},"canonical_sha256":"1b2f0fe414d87cc757f0f47a11f8a67f242a92eed8ead4f789e544368f6314e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b2f0fe414d87cc757f0f47a11f8a67f242a92eed8ead4f789e544368f6314e1","first_computed_at":"2026-05-18T00:04:07.148844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:07.148844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NvZDq4hL4YdX1XgC5loiO5E9awtrywmivJI9hfaspDLRE4sX7e/Y5ZJYerMTA8yVpgrj69AL6gR/ZDpvPCwVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:07.149488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c748cfb66bbf268df724d37a98ea53f2c171fbdaa6cd2a2c7c50f3fe7ee6b0d4","sha256:41b77d6cb985dcc640867ce2fdcca576e4dbfb0a43f1ac605563e72c49d2f6d8"],"state_sha256":"bd06cf2d6909396e1843d0aa22713c3442501ea159482732ba173c4525f7f738"}