{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TN6PNNGKVEK7FLYG2VSVAPSYJY","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":"777b2702a5b57069487ab9153622552f8f7a65e990f58e0675a4715eda0f77f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-24T12:38:07Z","title_canon_sha256":"0ef9a71df08b7227e2cfd61b10319423e9e80d24f3c80292012b3b2a86a96c1e"},"schema_version":"1.0","source":{"id":"1804.08991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08991","created_at":"2026-05-18T00:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08991v2","created_at":"2026-05-18T00:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08991","created_at":"2026-05-18T00:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"TN6PNNGKVEK7","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TN6PNNGKVEK7FLYG","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TN6PNNGK","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:cf54023d4f050301d373d5346729a9dde3c77817a12977cdf79b71b38fc0fb4b","target":"graph","created_at":"2026-05-18T00:02:25Z","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":"In this paper a relationship is established between the domination game and minimal edge cuts. It is proved that the game domination number of a connected graph can be bounded above in terms of the size of minimal edge cuts. In particular, if $C$ a minimum edge cut of a connected graph $G$, then $\\gamma_g(G) \\le \\gamma_g(G\\setminus C) + 2\\kappa'(G)$. Double-Staller graphs are introduced in order to show that this upper bound can be attained for graphs with a bridge. The obtained results are used to extend the family of known traceable graphs whose game domination numbers are at most one-half t","authors_text":"Douglas F. Rall, Sandi Klav\\v{z}ar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-24T12:38:07Z","title":"Domination game and minimal edge cuts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08991","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:d9a556c73c5971df3efcc0fb70c3431abb84dcfa8a6b6a9f3d05fc7cb31641ea","target":"record","created_at":"2026-05-18T00:02:25Z","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":"777b2702a5b57069487ab9153622552f8f7a65e990f58e0675a4715eda0f77f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-24T12:38:07Z","title_canon_sha256":"0ef9a71df08b7227e2cfd61b10319423e9e80d24f3c80292012b3b2a86a96c1e"},"schema_version":"1.0","source":{"id":"1804.08991","kind":"arxiv","version":2}},"canonical_sha256":"9b7cf6b4caa915f2af06d565503e584e0452eef5c7eefcb5b4072c78e7fac8ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b7cf6b4caa915f2af06d565503e584e0452eef5c7eefcb5b4072c78e7fac8ac","first_computed_at":"2026-05-18T00:02:25.202855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:25.202855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xO5+IvUTIMXUXSIrhAUeEiRfxrpZ19Es/aZBVJ77zrNUFY3mZsUsTSHc/baoql+ZEovliNNEGGFWiqQqzVcYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:25.203608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9a556c73c5971df3efcc0fb70c3431abb84dcfa8a6b6a9f3d05fc7cb31641ea","sha256:cf54023d4f050301d373d5346729a9dde3c77817a12977cdf79b71b38fc0fb4b"],"state_sha256":"0cbaa57500597477e4b41590f39589ab16f01c4ea07c7101caf7c7c221951d5e"}