{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MVEMV5MHNJUOHAJXKO6SEK77JK","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":"3d8d49f68e191a0184f70c70356adf677470f595d836bc5ea2cec8b0f5f3d079","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-04-21T12:15:06Z","title_canon_sha256":"50f106069d96fc455db713c7d4d2b13077ea8388bfdaea71edba6145cf6d8e42"},"schema_version":"1.0","source":{"id":"2004.09938","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.09938","created_at":"2026-07-05T06:06:50Z"},{"alias_kind":"arxiv_version","alias_value":"2004.09938v2","created_at":"2026-07-05T06:06:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.09938","created_at":"2026-07-05T06:06:50Z"},{"alias_kind":"pith_short_12","alias_value":"MVEMV5MHNJUO","created_at":"2026-07-05T06:06:50Z"},{"alias_kind":"pith_short_16","alias_value":"MVEMV5MHNJUOHAJX","created_at":"2026-07-05T06:06:50Z"},{"alias_kind":"pith_short_8","alias_value":"MVEMV5MH","created_at":"2026-07-05T06:06:50Z"}],"graph_snapshots":[{"event_id":"sha256:0af2dcb1936911f65cda0b41070fac982c60e5ef37d5472288afce571ff3b482","target":"graph","created_at":"2026-07-05T06:06:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.09938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\\geq2$ and $\\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-p","authors_text":"Catherine Greenhill, Luke Mathieson, Ryan L. Mann","cross_cats":["cs.DM","cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-04-21T12:15:06Z","title":"On the Parameterised Complexity of Induced Multipartite Graph Parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.09938","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:e8bcbce69a007c109b18cbc9b2b46ba812573555bb78c847b3d2da1c6aef3687","target":"record","created_at":"2026-07-05T06:06:50Z","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":"3d8d49f68e191a0184f70c70356adf677470f595d836bc5ea2cec8b0f5f3d079","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-04-21T12:15:06Z","title_canon_sha256":"50f106069d96fc455db713c7d4d2b13077ea8388bfdaea71edba6145cf6d8e42"},"schema_version":"1.0","source":{"id":"2004.09938","kind":"arxiv","version":2}},"canonical_sha256":"6548caf5876a68e3813753bd222bff4a97dbed4e7ac24abf8dadd75a14924b80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6548caf5876a68e3813753bd222bff4a97dbed4e7ac24abf8dadd75a14924b80","first_computed_at":"2026-07-05T06:06:50.875122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:06:50.875122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OXYDzEeHOH/rB+LAcyggKTppQCi8VBpIqLsqCC9F0tQiO+Knc7qkTp1eNAB0BMCQWay9YExXufQuewhsJnpvAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:06:50.875574Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.09938","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8bcbce69a007c109b18cbc9b2b46ba812573555bb78c847b3d2da1c6aef3687","sha256:0af2dcb1936911f65cda0b41070fac982c60e5ef37d5472288afce571ff3b482"],"state_sha256":"44d0d531f5d982c1a70191627c4e6d10507af1fa13ab76e1bdafa032b3a761e7"}