{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7NTACYMMTLJPS5NZFBPH7PMTAB","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":"bba1ec57ea0695b69125ae7107b47450dfddd877e9d4f21f14651e7c6caca34e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-13T15:36:20Z","title_canon_sha256":"a5f994cb16cfce04d045c8fc537aa414a5e40d4b1d1984479215da97f0b09527"},"schema_version":"1.0","source":{"id":"1706.04130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04130","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04130v1","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04130","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"7NTACYMMTLJP","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7NTACYMMTLJPS5NZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7NTACYMM","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:11baf5264f6227abe41f07037c83c21462342608fb9812ad93129a72e718a565","target":"graph","created_at":"2026-05-18T00:42:24Z","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":"A path cover is a decomposition of the edges of a graph into edge-disjoint simple paths. Gallai conjectured that every connected $n$-vertex graph has a path cover with at most $\\lceil n/2 \\rceil$ paths. We prove Gallai's conjecture for series-parallel graphs. For the class of planar 3-trees we show how to construct a path cover with at most $\\lfloor 5n/8 \\rfloor$ paths, which is an improvement over the best previously known bound of $\\lfloor 2n/3 \\rfloor$.","authors_text":"Andr\\'e Schulz, Lena Schlipf, Philipp Kindermann","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-13T15:36:20Z","title":"On Gallai's conjecture for series-parallel graphs and planar 3-trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04130","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":"sha256:7a652084958126a10355afdf169036d498ca66affd82a6e04203f24927c312e5","target":"record","created_at":"2026-05-18T00:42:24Z","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":"bba1ec57ea0695b69125ae7107b47450dfddd877e9d4f21f14651e7c6caca34e","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-13T15:36:20Z","title_canon_sha256":"a5f994cb16cfce04d045c8fc537aa414a5e40d4b1d1984479215da97f0b09527"},"schema_version":"1.0","source":{"id":"1706.04130","kind":"arxiv","version":1}},"canonical_sha256":"fb6601618c9ad2f975b9285e7fbd93006538c96d2ef5002b4599d11757a12953","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb6601618c9ad2f975b9285e7fbd93006538c96d2ef5002b4599d11757a12953","first_computed_at":"2026-05-18T00:42:24.443550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:24.443550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZsLljqYwXEgbv8ymmwBtoJHSbBRy83XBGFxYKKxxdoekHpS1GflfJ/WM8kh5gbx87oeyY+beovfc6jK20KODg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:24.444119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a652084958126a10355afdf169036d498ca66affd82a6e04203f24927c312e5","sha256:11baf5264f6227abe41f07037c83c21462342608fb9812ad93129a72e718a565"],"state_sha256":"0bf821977caf5ab7e2639d5245136f753f7f5fbdd42ad12f99779f66b9ef8d0e"}