{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NEIOYYNWM23NDSTX43OAZZHL6T","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":"308edcd23c0331359af6186b1af686a7b7480a129df41cfe4a2a09090d876d55","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-09T20:41:58Z","title_canon_sha256":"ba031b1822fb58dee87e5df8be4b8e36448d9dcc8effefdd9be404d5087422a7"},"schema_version":"1.0","source":{"id":"1311.2210","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2210","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2210v2","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2210","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"NEIOYYNWM23N","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NEIOYYNWM23NDSTX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NEIOYYNW","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:97cdb752e357597d77894bf94f92ddebe94c95210a9c99112d99ac8d836cfa16","target":"graph","created_at":"2026-05-18T03:06:54Z","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":"An edge-coloring of a multigraph $G$ with colors $1,\\ldots,t$ is called an interval $t$-coloring if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. In this note, we show that all Eulerian multigraphs with an odd number of edges have no interval coloring. We also give some methods for constructing of interval non-edge-colorable Eulerian multigraphs.","authors_text":"Petros A. Petrosyan","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-09T20:41:58Z","title":"On Interval Non-Edge-Colorable Eulerian Multigraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2210","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":"sha256:339f1599865a852f332335efd930ed2e662d2d9ee5048d8cecd7c87685de207f","target":"record","created_at":"2026-05-18T03:06:54Z","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":"308edcd23c0331359af6186b1af686a7b7480a129df41cfe4a2a09090d876d55","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-09T20:41:58Z","title_canon_sha256":"ba031b1822fb58dee87e5df8be4b8e36448d9dcc8effefdd9be404d5087422a7"},"schema_version":"1.0","source":{"id":"1311.2210","kind":"arxiv","version":2}},"canonical_sha256":"6910ec61b666b6d1ca77e6dc0ce4ebf4fa2752f6d3dcdcf53a0d13aac71bcab4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6910ec61b666b6d1ca77e6dc0ce4ebf4fa2752f6d3dcdcf53a0d13aac71bcab4","first_computed_at":"2026-05-18T03:06:54.103846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.103846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1qKO+o6Axp/VgVjB4J3Zlc72ESFuq9VVSkWRzZ4mHZAdaeYjH0l1DC2URj9bql10QL/4qV7gDf1CbsuH4s8GAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.104807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2210","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:339f1599865a852f332335efd930ed2e662d2d9ee5048d8cecd7c87685de207f","sha256:97cdb752e357597d77894bf94f92ddebe94c95210a9c99112d99ac8d836cfa16"],"state_sha256":"f76d2413e8371737294815751204c9aa201e85e68adc05cc1399f95d1b58d9c7"}