{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AC2OBOKG635YSVSK3IFBWFVVSD","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":"323885b41d299ee550522b0261132ad71c3eb8e65a6a09093ca25eb22f7b7a3b","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-01-16T20:11:07Z","title_canon_sha256":"6e4de66d3dd8f5d0c7316759ecde9889ed6f3bbb3f03c28d0e653f62937ac8d4"},"schema_version":"1.0","source":{"id":"1301.3811","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3811","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3811v2","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3811","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"AC2OBOKG635Y","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AC2OBOKG635YSVSK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AC2OBOKG","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:0ec75b977c403cada1b07c7dec77436facc15426f1e632ede0b38a17ce22e43f","target":"graph","created_at":"2026-05-18T03:36:05Z","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 graph $G$ with colors $1,...,t$ 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 1991 Erd\\H{o}s constructed a bipartite graph with 27 vertices and maximum degree 13 which has no interval coloring. Erd\\H{o}s's counterexample is the smallest (in a sense of maximum degree) known bipartite graph which is not interval colorable. On the other hand, in 1992 Hansen showed that all bipartite graphs with maximum degree at most 3 have an interval coloring. In this paper ","authors_text":"Hrant H. Khachatrian, Petros A. Petrosyan","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-01-16T20:11:07Z","title":"Interval non-edge-colorable bipartite graphs and multigraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3811","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":"sha256:77699238b3334a56a0afd156644c5468c78f07a7a278e196ae3546ccb5f3aa13","target":"record","created_at":"2026-05-18T03:36:05Z","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":"323885b41d299ee550522b0261132ad71c3eb8e65a6a09093ca25eb22f7b7a3b","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-01-16T20:11:07Z","title_canon_sha256":"6e4de66d3dd8f5d0c7316759ecde9889ed6f3bbb3f03c28d0e653f62937ac8d4"},"schema_version":"1.0","source":{"id":"1301.3811","kind":"arxiv","version":2}},"canonical_sha256":"00b4e0b946f6fb89564ada0a1b16b590cef2f2cf3c2c9005ffa8c0d9f1f61a99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00b4e0b946f6fb89564ada0a1b16b590cef2f2cf3c2c9005ffa8c0d9f1f61a99","first_computed_at":"2026-05-18T03:36:05.945480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:05.945480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZOzaI6iP8EI/kvq6fKfC7jXBs/FkSCgAbrcigtOWnWgGbzcWdWr4mDUWSB1CbkLWn+SymxqKBlh3Uvu/fI8oBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:05.946164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3811","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77699238b3334a56a0afd156644c5468c78f07a7a278e196ae3546ccb5f3aa13","sha256:0ec75b977c403cada1b07c7dec77436facc15426f1e632ede0b38a17ce22e43f"],"state_sha256":"1dcf62fc52d7e78629c37fc27413fa4303275cb0f0d3592c882e920700573298"}