{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7QJUXE5N35QTYLJORR3HIL2FBG","short_pith_number":"pith:7QJUXE5N","schema_version":"1.0","canonical_sha256":"fc134b93addf613c2d2e8c76742f4509a545e26ad02d337b39b8bc56100361b9","source":{"kind":"arxiv","id":"1303.1039","version":1},"attestation_state":"computed","paper":{"title":"On interval edge-colorings of outerplanar graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Petros A. Petrosyan","submitted_at":"2013-03-05T14:08:05Z","abstract_excerpt":"An edge-coloring of a graph $G$ 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. A graph $G$ is interval colorable if it has an interval $t$-coloring for some positive integer $t$. For an interval colorable graph $G$, the least value of $t$ for which $G$ has an interval $t$-coloring is denoted by $w(G)$. A graph $G$ is outerplanar if it can be embedded in the plane so that all its vertices lie on the same (unbounded) face. In this paper we show that if $G$ is "},"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":"1303.1039","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-03-05T14:08:05Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3aca98d16c0aaea03fe9d7f4d481c1c4740ae0b287f042985d7f8eb7476ded6a","abstract_canon_sha256":"9635c884614a66e408796e5c2c32b42f576a39cd9b33dc8c6bdbc064e724caa5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:45.713673Z","signature_b64":"EI+dqjVOU+d083YDmO/r7aWDTOuykAduAtwjVdI0lX8VmIz28HJxVE6P8YTLLTvPQfcH4XxvfIJE35OdACEzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc134b93addf613c2d2e8c76742f4509a545e26ad02d337b39b8bc56100361b9","last_reissued_at":"2026-05-18T03:31:45.712975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:45.712975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On interval edge-colorings of outerplanar graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Petros A. Petrosyan","submitted_at":"2013-03-05T14:08:05Z","abstract_excerpt":"An edge-coloring of a graph $G$ 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. A graph $G$ is interval colorable if it has an interval $t$-coloring for some positive integer $t$. For an interval colorable graph $G$, the least value of $t$ for which $G$ has an interval $t$-coloring is denoted by $w(G)$. A graph $G$ is outerplanar if it can be embedded in the plane so that all its vertices lie on the same (unbounded) face. In this paper we show that if $G$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1039","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.1039","created_at":"2026-05-18T03:31:45.713060+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1039v1","created_at":"2026-05-18T03:31:45.713060+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1039","created_at":"2026-05-18T03:31:45.713060+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QJUXE5N35QT","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QJUXE5N35QTYLJO","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QJUXE5N","created_at":"2026-05-18T12:27:36.564083+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG","json":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG.json","graph_json":"https://pith.science/api/pith-number/7QJUXE5N35QTYLJORR3HIL2FBG/graph.json","events_json":"https://pith.science/api/pith-number/7QJUXE5N35QTYLJORR3HIL2FBG/events.json","paper":"https://pith.science/paper/7QJUXE5N"},"agent_actions":{"view_html":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG","download_json":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG.json","view_paper":"https://pith.science/paper/7QJUXE5N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1039&json=true","fetch_graph":"https://pith.science/api/pith-number/7QJUXE5N35QTYLJORR3HIL2FBG/graph.json","fetch_events":"https://pith.science/api/pith-number/7QJUXE5N35QTYLJORR3HIL2FBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG/action/storage_attestation","attest_author":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG/action/author_attestation","sign_citation":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG/action/citation_signature","submit_replication":"https://pith.science/pith/7QJUXE5N35QTYLJORR3HIL2FBG/action/replication_record"}},"created_at":"2026-05-18T03:31:45.713060+00:00","updated_at":"2026-05-18T03:31:45.713060+00:00"}