{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RCZSHPSBSUL66X6SEEM7GCN4A7","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":"ea118199bd015733945a71bc31d1840d3cc012f07b1cd34b2138d09e01f939ce","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-23T17:27:15Z","title_canon_sha256":"0f91c71abd41cecb1c434eadbc1eb38dc1eb1227d1aaf63b0a1c5f0eb34fa1d0"},"schema_version":"1.0","source":{"id":"1102.4802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4802","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4802v1","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4802","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"RCZSHPSBSUL6","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCZSHPSBSUL66X6S","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCZSHPSB","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:a31f3dd2f8715fe88c354a6b4bc94ff70e13e33e7c06b984aefde3fb7d3c20a0","target":"graph","created_at":"2026-05-18T00:08:31Z","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":"In 2006, Suzuki, and Akbari & Alipour independently presented a necessary and sufficient condition for edge-colored graphs to have a heterochromatic spanning tree, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors. In this paper, we propose $f$-chromatic graphs as a generalization of heterochromatic graphs. An edge-colored graph is $f$-chromatic if each color $c$ appears on at most $f(c)$ edges. We also present a necessary and sufficient condition for edge-colored graphs to have an $f$-chromatic spanning forest with exactly $m$ components. Moreover, usin","authors_text":"Kazuhiro Suzuki","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-23T17:27:15Z","title":"A generalization of heterochromatic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4802","kind":"arxiv","version":1},"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":"sha256:3e7005d08f6e3e6341de2eafc4f40c4de9822785b4aa53aa0c8b5f02eb8b1759","target":"record","created_at":"2026-05-18T00:08:31Z","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":"ea118199bd015733945a71bc31d1840d3cc012f07b1cd34b2138d09e01f939ce","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-23T17:27:15Z","title_canon_sha256":"0f91c71abd41cecb1c434eadbc1eb38dc1eb1227d1aaf63b0a1c5f0eb34fa1d0"},"schema_version":"1.0","source":{"id":"1102.4802","kind":"arxiv","version":1}},"canonical_sha256":"88b323be419517ef5fd22119f309bc07d61ed18c08e2e9abf3166380be790a94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b323be419517ef5fd22119f309bc07d61ed18c08e2e9abf3166380be790a94","first_computed_at":"2026-05-18T00:08:31.869129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:31.869129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HtqGE4EjbaGONJo6u5uLIXwPJ2euj7rY+kDb6xZXTML2F+Bk2XZzfAGRvyTC0ceXcpyIQUQCGRkUkCSJsysRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:31.869757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e7005d08f6e3e6341de2eafc4f40c4de9822785b4aa53aa0c8b5f02eb8b1759","sha256:a31f3dd2f8715fe88c354a6b4bc94ff70e13e33e7c06b984aefde3fb7d3c20a0"],"state_sha256":"f48cd02e23fd8ce3ed42f00ced62c1f6eaacad05dde58a8ccb73906ecb702dba"}