{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F36QJPOPFXQVHUIVH6SV4ZGHKD","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":"2aac27abc0da2542d1ab10958085e56f88d3a4614ab84c908fdb459be260a9bc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-04T14:32:48Z","title_canon_sha256":"0860b710195d2b488079431b6c79e1082a920ae29c4470e4a51e804d0baa797f"},"schema_version":"1.0","source":{"id":"1904.02581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02581","created_at":"2026-05-17T23:47:01Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02581v2","created_at":"2026-05-17T23:47:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02581","created_at":"2026-05-17T23:47:01Z"},{"alias_kind":"pith_short_12","alias_value":"F36QJPOPFXQV","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"F36QJPOPFXQVHUIV","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"F36QJPOP","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:b60b536cd6bb9f7ab75b5045032e0e06b6a93bf50c3340a59b49b561679175eb","target":"graph","created_at":"2026-05-17T23:47:01Z","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":"Supergrid graphs contain grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for general supergrid graphs were known to be NP-complete. A graph is called Hamiltonian if it contains a Hamiltonian cycle, and is said to be Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices in it. In this paper, we first prove that every L-shaped supergrid graph always contains a Hamiltonian cycle except one trivial condition. We then verify the Hamiltonian connectivity of L-shaped supergrid graphs except few conditions. The Ham","authors_text":"Fatemeh Keshavarz-Kohjerdi, Ruo-Wei Hung","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-04T14:32:48Z","title":"The Hamiltonicity, Hamiltonian Connectivity, and Longest (s, t)-path of L-shaped Supergrid Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02581","kind":"arxiv","version":2},"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":"sha256:2aed48de084ad9520d7f9f2c303da170ba457d794d8663b333586e6e89725b65","target":"record","created_at":"2026-05-17T23:47:01Z","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":"2aac27abc0da2542d1ab10958085e56f88d3a4614ab84c908fdb459be260a9bc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-04T14:32:48Z","title_canon_sha256":"0860b710195d2b488079431b6c79e1082a920ae29c4470e4a51e804d0baa797f"},"schema_version":"1.0","source":{"id":"1904.02581","kind":"arxiv","version":2}},"canonical_sha256":"2efd04bdcf2de153d1153fa55e64c750e2f9e802056064d93d62fd2b975a07ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2efd04bdcf2de153d1153fa55e64c750e2f9e802056064d93d62fd2b975a07ed","first_computed_at":"2026-05-17T23:47:01.492686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:01.492686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jYbJd4CXSG7/aGfEdXm4XB9Eg9PN40mW0oODHQaayXUMlLkgfSjtHMNbYlRQ/mEzOuUYoobmtSjsNc8if0VNBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:01.493389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2aed48de084ad9520d7f9f2c303da170ba457d794d8663b333586e6e89725b65","sha256:b60b536cd6bb9f7ab75b5045032e0e06b6a93bf50c3340a59b49b561679175eb"],"state_sha256":"d339b91078b058b79aa4a87e0889ccae179e8e05b0ee1d54e1959d2f57c8ff63"}