{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HSK55ISOUDVWOAVETXTVOL7WEU","short_pith_number":"pith:HSK55ISO","schema_version":"1.0","canonical_sha256":"3c95dea24ea0eb6702a49de7572ff6252a34f5dff0ef524ad2d59bf307b9017e","source":{"kind":"arxiv","id":"1507.08456","version":1},"attestation_state":"computed","paper":{"title":"On The Chromatic Number of Matching Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hossein Hajiabolhassan, Meysam Alishahi","submitted_at":"2015-07-30T11:12:10Z","abstract_excerpt":"In an earlier paper, the present authors (2013) introduced the altermatic number of graphs and used Tucker's Lemma, an equivalent combinatorial version of the Borsuk-Ulam Theorem, to show that the altermatic number is a lower bound for the chromatic number. A matching graph has the set of all matchings of a specified size of a graph as vertex set and two vertices are adjacent if the corresponding matchings are edge-disjoint. It is known that the Kneser graphs, the Schrijver graphs, and the permutation graphs can be represented by matching graphs. In this paper, as a generalization of the well-"},"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":"1507.08456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-30T11:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"94d36a30d00cf5638b8f4157bb5bb7e5dcad9371ea55efbc2a465f8d2101246a","abstract_canon_sha256":"d2eab817ee9d95488dee0ba3b230c5c65f07ea1540c096677ab295223c6f08ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:06.408418Z","signature_b64":"awH+26O7WUxqMWbseLlWPXvhPxcuy4C+wdSjjT+I0ewSk514XqAKpHm8YYBpib+hRj0uVPm8l4WTF1FN4dv0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c95dea24ea0eb6702a49de7572ff6252a34f5dff0ef524ad2d59bf307b9017e","last_reissued_at":"2026-05-18T01:36:06.407917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:06.407917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On The Chromatic Number of Matching Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hossein Hajiabolhassan, Meysam Alishahi","submitted_at":"2015-07-30T11:12:10Z","abstract_excerpt":"In an earlier paper, the present authors (2013) introduced the altermatic number of graphs and used Tucker's Lemma, an equivalent combinatorial version of the Borsuk-Ulam Theorem, to show that the altermatic number is a lower bound for the chromatic number. A matching graph has the set of all matchings of a specified size of a graph as vertex set and two vertices are adjacent if the corresponding matchings are edge-disjoint. It is known that the Kneser graphs, the Schrijver graphs, and the permutation graphs can be represented by matching graphs. In this paper, as a generalization of the well-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08456","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":"1507.08456","created_at":"2026-05-18T01:36:06.408004+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.08456v1","created_at":"2026-05-18T01:36:06.408004+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08456","created_at":"2026-05-18T01:36:06.408004+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSK55ISOUDVW","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSK55ISOUDVWOAVE","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSK55ISO","created_at":"2026-05-18T12:29:25.134429+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/HSK55ISOUDVWOAVETXTVOL7WEU","json":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU.json","graph_json":"https://pith.science/api/pith-number/HSK55ISOUDVWOAVETXTVOL7WEU/graph.json","events_json":"https://pith.science/api/pith-number/HSK55ISOUDVWOAVETXTVOL7WEU/events.json","paper":"https://pith.science/paper/HSK55ISO"},"agent_actions":{"view_html":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU","download_json":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU.json","view_paper":"https://pith.science/paper/HSK55ISO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.08456&json=true","fetch_graph":"https://pith.science/api/pith-number/HSK55ISOUDVWOAVETXTVOL7WEU/graph.json","fetch_events":"https://pith.science/api/pith-number/HSK55ISOUDVWOAVETXTVOL7WEU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU/action/storage_attestation","attest_author":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU/action/author_attestation","sign_citation":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU/action/citation_signature","submit_replication":"https://pith.science/pith/HSK55ISOUDVWOAVETXTVOL7WEU/action/replication_record"}},"created_at":"2026-05-18T01:36:06.408004+00:00","updated_at":"2026-05-18T01:36:06.408004+00:00"}