{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Q3NLCP5QGV76W6YYWOVCY7Y2UA","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":"a279e2fbbd9a9da9d681afc77d3880b139bd2ec15f5df5d0b3f6c9f339990d87","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-01-11T13:57:33Z","title_canon_sha256":"98bbd403ead6887cfa5c0f0cdb8b70e9b4c3b9cc9c8c322a00da414f35733c89"},"schema_version":"1.0","source":{"id":"1901.03582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03582","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03582v1","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03582","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"Q3NLCP5QGV76","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q3NLCP5QGV76W6YY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q3NLCP5Q","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:84ab304c0bdd296c5c543ae33cb7c1878eb1a0e617c1a92b73d7efe9ce9b038e","target":"graph","created_at":"2026-05-17T23:56:30Z","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 the NP-hard Edge Dominating Set problem (EDS) we are given a graph $G=(V,E)$ and an integer $k$, and need to determine whether there is a set $F\\subseteq E$ of at most $k$ edges that are incident with all (other) edges of $G$. It is known that this problem is fixed-parameter tractable and admits a polynomial kernel when parameterized by $k$. A caveat for this parameter is that it needs to be large, i.e., at least equal to half the size of a maximum matching of $G$, for instances not to be trivially negative. Motivated by this, we study the existence of polynomial kernels for EDS when parame","authors_text":"Eva-Maria C. Hols, Stefan Kratsch","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-01-11T13:57:33Z","title":"On Kernelization for Edge Dominating Set under Structural Parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03582","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":"sha256:36f69b0f09541716fb10c45272d110661724d8540457c4ab415299a2844a53e6","target":"record","created_at":"2026-05-17T23:56:30Z","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":"a279e2fbbd9a9da9d681afc77d3880b139bd2ec15f5df5d0b3f6c9f339990d87","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-01-11T13:57:33Z","title_canon_sha256":"98bbd403ead6887cfa5c0f0cdb8b70e9b4c3b9cc9c8c322a00da414f35733c89"},"schema_version":"1.0","source":{"id":"1901.03582","kind":"arxiv","version":1}},"canonical_sha256":"86dab13fb0357feb7b18b3aa2c7f1aa02a66c4de3c831b6f4a01d275b6bd41b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86dab13fb0357feb7b18b3aa2c7f1aa02a66c4de3c831b6f4a01d275b6bd41b2","first_computed_at":"2026-05-17T23:56:30.874978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:30.874978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iwNYkWk4DNFvo4DVfnE09/sPsPHqF4I5n+KNyiYe2M+nN2TWKiUXfRaikP5s0la+R/mpIf70al65TWddxxieDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:30.875386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.03582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36f69b0f09541716fb10c45272d110661724d8540457c4ab415299a2844a53e6","sha256:84ab304c0bdd296c5c543ae33cb7c1878eb1a0e617c1a92b73d7efe9ce9b038e"],"state_sha256":"5a93e187e17388eac3da0afe78f92519c64b7602106fc8215d64c801e6594a6d"}