{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:F4W57L4Y3HVQFIQZWUWSSGLHQZ","short_pith_number":"pith:F4W57L4Y","schema_version":"1.0","canonical_sha256":"2f2ddfaf98d9eb02a219b52d29196786505c9e6c385e5c471b135d2c7a700123","source":{"kind":"arxiv","id":"1510.03381","version":1},"attestation_state":"computed","paper":{"title":"I,F-partitions of Sparse Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Axel Brandt, Derrick Stolee, Matthew Yancey, Michael Ferrara, Mohit Kumbhat, Sarah Loeb","submitted_at":"2015-10-12T18:20:35Z","abstract_excerpt":"A star $k$-coloring is a proper $k$-coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One method to produce a star 4-coloring is to partition the vertex set into a 2-independent set and a forest; such a partition is called an I,F-partition. We use a combination of potential functions and discharging to prove that every graph with maximum average degree less than $\\frac{5}{2}$ has an I,F-partition, which is sharp and answers a question of Cranston and West [A guide to the discharging method, "},"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":"1510.03381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-12T18:20:35Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"e202b5258cdcef33f1087d63e5db48331b10bb733f0c88e275a5e7d016f05980","abstract_canon_sha256":"9cc0cb9a9ad3dc3a49506a4afdb876cd47ddb1dc4e4803819d75f7c55ca9f6e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:26.405303Z","signature_b64":"ayjDr5/R2mWUvcUBo7M7ONqQpduwXpu99nApf9CbzEJ74rfS7ybBHv7LsjHeFXe7rs1XepLXIk605khz04PVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f2ddfaf98d9eb02a219b52d29196786505c9e6c385e5c471b135d2c7a700123","last_reissued_at":"2026-05-18T01:30:26.404665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:26.404665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"I,F-partitions of Sparse Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Axel Brandt, Derrick Stolee, Matthew Yancey, Michael Ferrara, Mohit Kumbhat, Sarah Loeb","submitted_at":"2015-10-12T18:20:35Z","abstract_excerpt":"A star $k$-coloring is a proper $k$-coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One method to produce a star 4-coloring is to partition the vertex set into a 2-independent set and a forest; such a partition is called an I,F-partition. We use a combination of potential functions and discharging to prove that every graph with maximum average degree less than $\\frac{5}{2}$ has an I,F-partition, which is sharp and answers a question of Cranston and West [A guide to the discharging method, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03381","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":"1510.03381","created_at":"2026-05-18T01:30:26.404747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03381v1","created_at":"2026-05-18T01:30:26.404747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03381","created_at":"2026-05-18T01:30:26.404747+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4W57L4Y3HVQ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4W57L4Y3HVQFIQZ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4W57L4Y","created_at":"2026-05-18T12:29:19.899920+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/F4W57L4Y3HVQFIQZWUWSSGLHQZ","json":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ.json","graph_json":"https://pith.science/api/pith-number/F4W57L4Y3HVQFIQZWUWSSGLHQZ/graph.json","events_json":"https://pith.science/api/pith-number/F4W57L4Y3HVQFIQZWUWSSGLHQZ/events.json","paper":"https://pith.science/paper/F4W57L4Y"},"agent_actions":{"view_html":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ","download_json":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ.json","view_paper":"https://pith.science/paper/F4W57L4Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03381&json=true","fetch_graph":"https://pith.science/api/pith-number/F4W57L4Y3HVQFIQZWUWSSGLHQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/F4W57L4Y3HVQFIQZWUWSSGLHQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ/action/storage_attestation","attest_author":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ/action/author_attestation","sign_citation":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ/action/citation_signature","submit_replication":"https://pith.science/pith/F4W57L4Y3HVQFIQZWUWSSGLHQZ/action/replication_record"}},"created_at":"2026-05-18T01:30:26.404747+00:00","updated_at":"2026-05-18T01:30:26.404747+00:00"}