{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S67JAVSYLDMBUJSSSZSC6NRD27","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":"ba87d86fc2847da8b5f67bf6f7a4fac62578eb04e5d0f20a78cabf2ca495371f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-29T22:44:52Z","title_canon_sha256":"612de04bd7692ef687cf3c22cca82f24a67cc297b3f1a62349721aac08fe6a33"},"schema_version":"1.0","source":{"id":"1301.7090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7090","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7090v1","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7090","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"pith_short_12","alias_value":"S67JAVSYLDMB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S67JAVSYLDMBUJSS","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S67JAVSY","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:0cf213210d66c452273680616bf835aed3d66c41e9017e5077cd991e37b23564","target":"graph","created_at":"2026-05-18T03:35:01Z","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":"For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring. This is the problem of coloring the vertices while ensuring that two vertices that are adjacent or have a common neighbor receive different colors. It is already known that planar graphs of girth at least 6 and of maximum degree D are list 2-distance (D+2)-colorable when D>=24 (Borodin and Ivanova (2009)) and 2-distance (D+2)-colorable when D>=18 (Borodin and Ivanova (2009)). We prove here that D>=17 suffices in both cases. More generally, we show that graphs with maximum average degree less than 3 an","authors_text":"Alexandre Pinlou, Benjamin L\\'ev\\^eque, Marthe Bonamy","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-29T22:44:52Z","title":"Graphs with maximum degree D at least 17 and maximum average degree less than 3 are list 2-distance (D+2)-colorable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7090","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":"sha256:5831c7a530717c483c4b23bfe1f52ea74d4d81b884eda1a35ccef5e866077e40","target":"record","created_at":"2026-05-18T03:35:01Z","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":"ba87d86fc2847da8b5f67bf6f7a4fac62578eb04e5d0f20a78cabf2ca495371f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-01-29T22:44:52Z","title_canon_sha256":"612de04bd7692ef687cf3c22cca82f24a67cc297b3f1a62349721aac08fe6a33"},"schema_version":"1.0","source":{"id":"1301.7090","kind":"arxiv","version":1}},"canonical_sha256":"97be90565858d81a265296642f3623d7dbbe4d70d6e7b3cad465f555ff29e757","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97be90565858d81a265296642f3623d7dbbe4d70d6e7b3cad465f555ff29e757","first_computed_at":"2026-05-18T03:35:01.324798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:01.324798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R6iCfoe90oE5QrG8NI/TuAdhyy4lVnn7pTnhFpH+7bp+fsItp/wg8ORI0WrGF5pqAMLCyoMs8vpLd0QmgSfjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:01.325656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5831c7a530717c483c4b23bfe1f52ea74d4d81b884eda1a35ccef5e866077e40","sha256:0cf213210d66c452273680616bf835aed3d66c41e9017e5077cd991e37b23564"],"state_sha256":"73b268674e6817b995347ba4039d1cf4ed7043e7dcdb8e24f912192eaa5b1578"}