{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7YB7OI3VRAVSZABDF455XBKKBR","short_pith_number":"pith:7YB7OI3V","schema_version":"1.0","canonical_sha256":"fe03f72375882b2c80232f3bdb854a0c4d703a1d3ced4a44500307a4d08469db","source":{"kind":"arxiv","id":"1504.06585","version":2},"attestation_state":"computed","paper":{"title":"Clique number of the square of a line graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ma{\\l}gorzata \\'Sleszy\\'nska-Nowak","submitted_at":"2015-04-24T18:04:45Z","abstract_excerpt":"An \\emph{edge coloring} of a graph $G$ is strong if each color class is an induced matching of $G$. The \\emph{strong chromatic index} of $G$, denoted by $\\chi _{s}^{\\prime }(G)$, is the minimum number of colors for which $G$ has a strong edge coloring. The strong chromatic index of $G$ is equal to the chromatic number of the square of the line graph of $G$. The chromatic number of the square of the line graph of $G$ is greater than or equal to the clique number of the square of the line graph of $G$, denoted by $\\omega(L)$.\n  In this note we prove that $\\omega(L) \\le 1.5 \\Delta_{G}^2$ for ever"},"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":"1504.06585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-24T18:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"db0182ff924ffbef209500fde6c326bdb64120b58b7a2276e01ccd52afd6b2da","abstract_canon_sha256":"1bee0ef946b4d80de87d842205845a837cfa6a2cfd0c915aa6725a7507e9c35e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:14.030097Z","signature_b64":"2KASq50DtiIdOruOa7/8z7h6F8ejH0BMPWbvZY6WgrNPZyveFO2vere+tDerAzR+VPlznIMFcR3Fuk7rrSWrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe03f72375882b2c80232f3bdb854a0c4d703a1d3ced4a44500307a4d08469db","last_reissued_at":"2026-05-18T02:17:14.029455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:14.029455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clique number of the square of a line graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ma{\\l}gorzata \\'Sleszy\\'nska-Nowak","submitted_at":"2015-04-24T18:04:45Z","abstract_excerpt":"An \\emph{edge coloring} of a graph $G$ is strong if each color class is an induced matching of $G$. The \\emph{strong chromatic index} of $G$, denoted by $\\chi _{s}^{\\prime }(G)$, is the minimum number of colors for which $G$ has a strong edge coloring. The strong chromatic index of $G$ is equal to the chromatic number of the square of the line graph of $G$. The chromatic number of the square of the line graph of $G$ is greater than or equal to the clique number of the square of the line graph of $G$, denoted by $\\omega(L)$.\n  In this note we prove that $\\omega(L) \\le 1.5 \\Delta_{G}^2$ for ever"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06585","kind":"arxiv","version":2},"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":"1504.06585","created_at":"2026-05-18T02:17:14.029557+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06585v2","created_at":"2026-05-18T02:17:14.029557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06585","created_at":"2026-05-18T02:17:14.029557+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YB7OI3VRAVS","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YB7OI3VRAVSZABD","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YB7OI3V","created_at":"2026-05-18T12:29:10.953037+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/7YB7OI3VRAVSZABDF455XBKKBR","json":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR.json","graph_json":"https://pith.science/api/pith-number/7YB7OI3VRAVSZABDF455XBKKBR/graph.json","events_json":"https://pith.science/api/pith-number/7YB7OI3VRAVSZABDF455XBKKBR/events.json","paper":"https://pith.science/paper/7YB7OI3V"},"agent_actions":{"view_html":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR","download_json":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR.json","view_paper":"https://pith.science/paper/7YB7OI3V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06585&json=true","fetch_graph":"https://pith.science/api/pith-number/7YB7OI3VRAVSZABDF455XBKKBR/graph.json","fetch_events":"https://pith.science/api/pith-number/7YB7OI3VRAVSZABDF455XBKKBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR/action/storage_attestation","attest_author":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR/action/author_attestation","sign_citation":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR/action/citation_signature","submit_replication":"https://pith.science/pith/7YB7OI3VRAVSZABDF455XBKKBR/action/replication_record"}},"created_at":"2026-05-18T02:17:14.029557+00:00","updated_at":"2026-05-18T02:17:14.029557+00:00"}