{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JN7FY5JW2QDOFOZR4LUN5STVYN","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":"b00b9be09e3e0546b705fb47c7ffd14399947936184e0c079e6c3f321f2170cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-28T22:31:49Z","title_canon_sha256":"ef938249eef77d6a38f4e773527a7db8d4f5ed4f5e005355f01ea1531f6521e9"},"schema_version":"1.0","source":{"id":"1903.12292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12292","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12292v1","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12292","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"pith_short_12","alias_value":"JN7FY5JW2QDO","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JN7FY5JW2QDOFOZR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JN7FY5JW","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:f1bc7f81f2445fd2b431b89a3906a53b8f3c7146700dd7b4ed8034ad7e891153","target":"graph","created_at":"2026-05-17T23:49:54Z","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":"Several domination results have been obtained for maximal outerplanar graphs (mops). The classical domination problem is to minimize the size of a set $S$ of vertices of an $n$-vertex graph $G$ such that $G - N[S]$, the graph obtained by deleting the closed neighborhood of $S$, is null. A classical result of Chv\\'{a}tal is that the minimum size is at most $n/3$ if $G$ is a mop. Here we consider a modification by allowing $G - N[S]$ to have isolated vertices and isolated edges only. Let $\\iota_1(G)$ denote the size of a smallest set $S$ for which this is achieved. We show that if $G$ is a mop o","authors_text":"Pawaton Kaemawichanurat, Peter Borg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-28T22:31:49Z","title":"Partial domination of maximal outerplanar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12292","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:ddd347cc3f7ed5278ab78d62d0504dd75e0fd32cfa6776c02e36d71d4e2cba9b","target":"record","created_at":"2026-05-17T23:49:54Z","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":"b00b9be09e3e0546b705fb47c7ffd14399947936184e0c079e6c3f321f2170cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-28T22:31:49Z","title_canon_sha256":"ef938249eef77d6a38f4e773527a7db8d4f5ed4f5e005355f01ea1531f6521e9"},"schema_version":"1.0","source":{"id":"1903.12292","kind":"arxiv","version":1}},"canonical_sha256":"4b7e5c7536d406e2bb31e2e8deca75c37a8d9dc42f2c6c9e78c9075b7e0dfaf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7e5c7536d406e2bb31e2e8deca75c37a8d9dc42f2c6c9e78c9075b7e0dfaf9","first_computed_at":"2026-05-17T23:49:54.401184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:54.401184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SMikBRI5HblVqaytpS0mMrX0kseE2ZCg7DPUCglpE/mL0eJigVJKSnsTcgqGyTwCERXzGpkaSbAxxHXlxx8wDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:54.401637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.12292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddd347cc3f7ed5278ab78d62d0504dd75e0fd32cfa6776c02e36d71d4e2cba9b","sha256:f1bc7f81f2445fd2b431b89a3906a53b8f3c7146700dd7b4ed8034ad7e891153"],"state_sha256":"a43da24c757ee5f420d0371f55157626aa1257a5ee5b0dc71d242ae223e099e3"}