{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZTHB3UTFQCXN46UNTP4P3HN44A","short_pith_number":"pith:ZTHB3UTF","schema_version":"1.0","canonical_sha256":"ccce1dd26580aede7a8d9bf8fd9dbce02cf237cb4aa6c4d9202e53f1e3366bed","source":{"kind":"arxiv","id":"1302.3404","version":1},"attestation_state":"computed","paper":{"title":"The min-max edge q-coloring problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexandru Popa, Tommi Larjomaa","submitted_at":"2013-02-14T14:07:55Z","abstract_excerpt":"In this paper we introduce and study a new problem named \\emph{min-max edge $q$-coloring} which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer $q$. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most $q$ different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: \n1. Min-max edge $q$-coloring is NP-hard, for any $q \\ge 2$.\n2. A polynomial time exact algorithm"},"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":"1302.3404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-02-14T14:07:55Z","cross_cats_sorted":[],"title_canon_sha256":"75abee56843d64473dfb3f28ea19bffba4de9b856c2c9014c28b8e0bb5771fd6","abstract_canon_sha256":"675466ce6887722a7a1cc6fd6659b13da68b6db7e2bd30709408bc88fcbbf569"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:39.023958Z","signature_b64":"lHRM3gPrbt1kVcekvGZY9eVZXoGZUYAS74C0DN/91tm3D55nhqmuZvrZKv0RIJiCtvBfia0h/9dp8dKu2TZ8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccce1dd26580aede7a8d9bf8fd9dbce02cf237cb4aa6c4d9202e53f1e3366bed","last_reissued_at":"2026-05-18T03:33:39.023422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:39.023422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The min-max edge q-coloring problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexandru Popa, Tommi Larjomaa","submitted_at":"2013-02-14T14:07:55Z","abstract_excerpt":"In this paper we introduce and study a new problem named \\emph{min-max edge $q$-coloring} which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer $q$. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most $q$ different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: \n1. Min-max edge $q$-coloring is NP-hard, for any $q \\ge 2$.\n2. A polynomial time exact algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3404","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":"1302.3404","created_at":"2026-05-18T03:33:39.023500+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.3404v1","created_at":"2026-05-18T03:33:39.023500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3404","created_at":"2026-05-18T03:33:39.023500+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZTHB3UTFQCXN","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZTHB3UTFQCXN46UN","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZTHB3UTF","created_at":"2026-05-18T12:28:09.283467+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/ZTHB3UTFQCXN46UNTP4P3HN44A","json":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A.json","graph_json":"https://pith.science/api/pith-number/ZTHB3UTFQCXN46UNTP4P3HN44A/graph.json","events_json":"https://pith.science/api/pith-number/ZTHB3UTFQCXN46UNTP4P3HN44A/events.json","paper":"https://pith.science/paper/ZTHB3UTF"},"agent_actions":{"view_html":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A","download_json":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A.json","view_paper":"https://pith.science/paper/ZTHB3UTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.3404&json=true","fetch_graph":"https://pith.science/api/pith-number/ZTHB3UTFQCXN46UNTP4P3HN44A/graph.json","fetch_events":"https://pith.science/api/pith-number/ZTHB3UTFQCXN46UNTP4P3HN44A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A/action/storage_attestation","attest_author":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A/action/author_attestation","sign_citation":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A/action/citation_signature","submit_replication":"https://pith.science/pith/ZTHB3UTFQCXN46UNTP4P3HN44A/action/replication_record"}},"created_at":"2026-05-18T03:33:39.023500+00:00","updated_at":"2026-05-18T03:33:39.023500+00:00"}