{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5Q2X5VXB3TMPS35MZL4NRZM2KN","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":"f6c9bad0eaa2dffb7d27f6f6a395b64a76d0edf046fb412d4feca1d1cfab4008","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-06-14T14:38:07Z","title_canon_sha256":"0cfafef8f6178ccb1caf506ba442050d5b496b6bb0756a4c3dd63e80530f0ed0"},"schema_version":"1.0","source":{"id":"1606.04394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04394","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04394v1","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04394","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"5Q2X5VXB3TMP","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5Q2X5VXB3TMPS35M","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5Q2X5VXB","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:d7d4a9d439b88e028552f2363412fa40a3364c1ee173457f3f356222e8fefcce","target":"graph","created_at":"2026-05-18T01:12:25Z","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":"An $({\\cal I},{\\cal F}_d)$-partition of a graph is a partition of the vertices of the graph into two sets $I$ and $F$, such that $I$ is an independent set and $F$ induces a forest of maximum degree at most $d$. We show that for all $M<3$ and $d \\ge \\frac{2}{3-M} - 2$, if a graph has maximum average degree less than $M$, then it has an $({\\cal I},{\\cal F}_d)$-partition. Additionally, we prove that for all $\\frac{8}{3} \\le M < 3$ and $d \\ge \\frac{1}{3-M}$, if a graph has maximum average degree less than $M$ then it has an $({\\cal I},{\\cal F}_d)$-partition.","authors_text":"Alexandre Pinlou, Fran\\c{c}ois Dross, Mickael Montassier","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-06-14T14:38:07Z","title":"Partitioning sparse graphs into an independent set and a forest of bounded degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04394","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:e1595895a90505a273bda1168195646a5743870a064baa3d926ea91e87b4f160","target":"record","created_at":"2026-05-18T01:12:25Z","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":"f6c9bad0eaa2dffb7d27f6f6a395b64a76d0edf046fb412d4feca1d1cfab4008","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-06-14T14:38:07Z","title_canon_sha256":"0cfafef8f6178ccb1caf506ba442050d5b496b6bb0756a4c3dd63e80530f0ed0"},"schema_version":"1.0","source":{"id":"1606.04394","kind":"arxiv","version":1}},"canonical_sha256":"ec357ed6e1dcd8f96faccaf8d8e59a537a628432c0db2123296be2f0ac2378b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec357ed6e1dcd8f96faccaf8d8e59a537a628432c0db2123296be2f0ac2378b8","first_computed_at":"2026-05-18T01:12:25.657400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:25.657400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LjL1M6AvwzA8q9gtoaVLJlR3t+RVrGm8A2GbLSs2g2AOggsmelrknsJwM8zoDexmivx8ouBqNhv+re4951lUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:25.657785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1595895a90505a273bda1168195646a5743870a064baa3d926ea91e87b4f160","sha256:d7d4a9d439b88e028552f2363412fa40a3364c1ee173457f3f356222e8fefcce"],"state_sha256":"3775660f5a68cc446fb45d3376bdae3843e08c21d1e09a80bdcf7cc0df1ce3a4"}