{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UJPSJI45V5HWSMJIHL34UGRWDF","short_pith_number":"pith:UJPSJI45","canonical_record":{"source":{"id":"1809.02799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-08T13:20:01Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"95ead7cbb75c18d940a54443f94a6cfe963d2c78f252863f15f8e11ce82976eb","abstract_canon_sha256":"e7d58c02b88a6133fcfc3486ed41428c4256ccc4ab875dbe7ab7919a017ff9cd"},"schema_version":"1.0"},"canonical_sha256":"a25f24a39daf4f6931283af7ca1a361978f7595f0ebb1d433afc55e54106645c","source":{"kind":"arxiv","id":"1809.02799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02799","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02799v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02799","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"UJPSJI45V5HW","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UJPSJI45V5HWSMJI","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UJPSJI45","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UJPSJI45V5HWSMJIHL34UGRWDF","target":"record","payload":{"canonical_record":{"source":{"id":"1809.02799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-08T13:20:01Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"95ead7cbb75c18d940a54443f94a6cfe963d2c78f252863f15f8e11ce82976eb","abstract_canon_sha256":"e7d58c02b88a6133fcfc3486ed41428c4256ccc4ab875dbe7ab7919a017ff9cd"},"schema_version":"1.0"},"canonical_sha256":"a25f24a39daf4f6931283af7ca1a361978f7595f0ebb1d433afc55e54106645c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:15.254181Z","signature_b64":"ZVcitnR/OAhqUt1e3j4cBq74dGFRUv/SFH/zoQRGe9J6ugvpXEfCqtsbpEPjOHSTAJ4IJvuSyxZR7/s1jOypBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a25f24a39daf4f6931283af7ca1a361978f7595f0ebb1d433afc55e54106645c","last_reissued_at":"2026-05-18T00:06:15.253541Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:15.253541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.02799","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zdt+PVDkhV+FveMcpN49Z0FFvrw4CxEAYOp6bNp9IjzK/YLALt7wp1VSke5u6sPneWzwTcCSGUBa5LN2uFiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:39:27.000109Z"},"content_sha256":"bbdcd2f2937cb52713e90468832b9828bbac2ab09c4972ce10752b0f9f9aa517","schema_version":"1.0","event_id":"sha256:bbdcd2f2937cb52713e90468832b9828bbac2ab09c4972ce10752b0f9f9aa517"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UJPSJI45V5HWSMJIHL34UGRWDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the edge partition of graphs containing either a light edge or an alternating 2-cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bei Niu, Xin Zhang","submitted_at":"2018-09-08T13:20:01Z","abstract_excerpt":"Let $\\mathcal{G}_{\\alpha}$ be a hereditary graph class (i.e, every subgraph of $G_{\\alpha}\\in \\mathcal{G}_{\\alpha}$ belongs to $\\mathcal{G}_{\\alpha}$) such that every graph $G_{\\alpha}$ in $\\mathcal{G}_{\\alpha}$ has minimum degree at most 1, or contains either an edge $uv$ such that $d_{G_{\\alpha}}(u)+d_{G_{\\alpha}}(v)\\leq \\alpha$ or a 2-alternating cycle. It is proved that every graph in $\\mathcal{G}_{\\alpha}$ ($\\alpha\\geq 5$) with maximum degree $\\Delta$ can be edge-partitioned into two forests $F_1$, $F_2$ and a subgraph $H$ such that $\\Delta(F_i)\\leq \\max\\{2,\\lceil\\frac{\\Delta-\\alpha+6}{2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02799","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xG+YShzd6dukyd8N4V5oAudm6rWJhZCT2L9TS9yS8Ftd4ue6P9N7hW8U1JtlJrkw+pJhDosvr6QB/RmZ6Gg6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:39:27.000841Z"},"content_sha256":"1fa1d9b77f7a7c1eea83722f6edbb95f0df7177ca47fc1f6027648d4d526dac1","schema_version":"1.0","event_id":"sha256:1fa1d9b77f7a7c1eea83722f6edbb95f0df7177ca47fc1f6027648d4d526dac1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJPSJI45V5HWSMJIHL34UGRWDF/bundle.json","state_url":"https://pith.science/pith/UJPSJI45V5HWSMJIHL34UGRWDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJPSJI45V5HWSMJIHL34UGRWDF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T07:39:27Z","links":{"resolver":"https://pith.science/pith/UJPSJI45V5HWSMJIHL34UGRWDF","bundle":"https://pith.science/pith/UJPSJI45V5HWSMJIHL34UGRWDF/bundle.json","state":"https://pith.science/pith/UJPSJI45V5HWSMJIHL34UGRWDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJPSJI45V5HWSMJIHL34UGRWDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UJPSJI45V5HWSMJIHL34UGRWDF","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":"e7d58c02b88a6133fcfc3486ed41428c4256ccc4ab875dbe7ab7919a017ff9cd","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-08T13:20:01Z","title_canon_sha256":"95ead7cbb75c18d940a54443f94a6cfe963d2c78f252863f15f8e11ce82976eb"},"schema_version":"1.0","source":{"id":"1809.02799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02799","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02799v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02799","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"UJPSJI45V5HW","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UJPSJI45V5HWSMJI","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UJPSJI45","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:1fa1d9b77f7a7c1eea83722f6edbb95f0df7177ca47fc1f6027648d4d526dac1","target":"graph","created_at":"2026-05-18T00:06:15Z","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":"Let $\\mathcal{G}_{\\alpha}$ be a hereditary graph class (i.e, every subgraph of $G_{\\alpha}\\in \\mathcal{G}_{\\alpha}$ belongs to $\\mathcal{G}_{\\alpha}$) such that every graph $G_{\\alpha}$ in $\\mathcal{G}_{\\alpha}$ has minimum degree at most 1, or contains either an edge $uv$ such that $d_{G_{\\alpha}}(u)+d_{G_{\\alpha}}(v)\\leq \\alpha$ or a 2-alternating cycle. It is proved that every graph in $\\mathcal{G}_{\\alpha}$ ($\\alpha\\geq 5$) with maximum degree $\\Delta$ can be edge-partitioned into two forests $F_1$, $F_2$ and a subgraph $H$ such that $\\Delta(F_i)\\leq \\max\\{2,\\lceil\\frac{\\Delta-\\alpha+6}{2}","authors_text":"Bei Niu, Xin Zhang","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-08T13:20:01Z","title":"A note on the edge partition of graphs containing either a light edge or an alternating 2-cycle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02799","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:bbdcd2f2937cb52713e90468832b9828bbac2ab09c4972ce10752b0f9f9aa517","target":"record","created_at":"2026-05-18T00:06:15Z","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":"e7d58c02b88a6133fcfc3486ed41428c4256ccc4ab875dbe7ab7919a017ff9cd","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-08T13:20:01Z","title_canon_sha256":"95ead7cbb75c18d940a54443f94a6cfe963d2c78f252863f15f8e11ce82976eb"},"schema_version":"1.0","source":{"id":"1809.02799","kind":"arxiv","version":1}},"canonical_sha256":"a25f24a39daf4f6931283af7ca1a361978f7595f0ebb1d433afc55e54106645c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a25f24a39daf4f6931283af7ca1a361978f7595f0ebb1d433afc55e54106645c","first_computed_at":"2026-05-18T00:06:15.253541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:15.253541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZVcitnR/OAhqUt1e3j4cBq74dGFRUv/SFH/zoQRGe9J6ugvpXEfCqtsbpEPjOHSTAJ4IJvuSyxZR7/s1jOypBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:15.254181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbdcd2f2937cb52713e90468832b9828bbac2ab09c4972ce10752b0f9f9aa517","sha256:1fa1d9b77f7a7c1eea83722f6edbb95f0df7177ca47fc1f6027648d4d526dac1"],"state_sha256":"6bbca610dc53b7cb6a9272cca267a2c7538a936b93712749da2e69d01af4c26e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5FVORqZdDhnkNibfkVUPeuFuoaP7q8PbsWjAopSHJRPiy7p092welT91bxipDly4jGAUF3BwOEmzhs0XaIV8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:39:27.004823Z","bundle_sha256":"e842e7a675d6f455d30db9502df2e837b27d7024d76914ef46630f0c8a8c4c3c"}}