{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4V37JKWOONSX3MV2INUQ2V6HRT","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":"0ec4b792c2601b564e8400a11f9f10014042ee90be5e71ae21ace70b11be4e92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-14T15:45:20Z","title_canon_sha256":"fa12042e73bfc15ea829dac9bd940575806460ebfab601972b72c12e893811a3"},"schema_version":"1.0","source":{"id":"1903.06087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06087","created_at":"2026-05-17T23:51:15Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06087v1","created_at":"2026-05-17T23:51:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06087","created_at":"2026-05-17T23:51:15Z"},{"alias_kind":"pith_short_12","alias_value":"4V37JKWOONSX","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4V37JKWOONSX3MV2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4V37JKWO","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:d189a758be0755f2e1c2f1c7198866bf929b2fc4875153307baf231f67ac33af","target":"graph","created_at":"2026-05-17T23:51:15Z","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":"Given a graph $G$, the strong clique number $\\omega_2'(G)$ of $G$ is the cardinality of a largest collection of edges every pair of which are incident or connected by an edge in $G$. We study the strong clique number of graphs missing some set of cycle lengths. For a graph $G$ of large enough maximum degree $\\Delta$, we show among other results the following: $\\omega_2'(G)\\le5\\Delta^2/4$ if $G$ is triangle-free; $\\omega_2'(G)\\le3(\\Delta-1)$ if $G$ is $C_4$-free; $\\omega_2'(G)\\le\\Delta^2$ if $G$ is $C_{2k+1}$-free for some $k\\ge 2$. These bounds are attained by natural extremal examples. Our wo","authors_text":"Fran\\c{c}ois Pirot, Ross J. Kang, Wouter Cames van Batenburg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-14T15:45:20Z","title":"Strong cliques and forbidden cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06087","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":"sha256:7ce516b0ba5587328883459030e7b81c1c691863a7281b9188a3abc90e85c291","target":"record","created_at":"2026-05-17T23:51:15Z","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":"0ec4b792c2601b564e8400a11f9f10014042ee90be5e71ae21ace70b11be4e92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-14T15:45:20Z","title_canon_sha256":"fa12042e73bfc15ea829dac9bd940575806460ebfab601972b72c12e893811a3"},"schema_version":"1.0","source":{"id":"1903.06087","kind":"arxiv","version":1}},"canonical_sha256":"e577f4aace73657db2ba43690d57c78cfaaf71c14c205ddd86b2aedfa891a065","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e577f4aace73657db2ba43690d57c78cfaaf71c14c205ddd86b2aedfa891a065","first_computed_at":"2026-05-17T23:51:15.416468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:15.416468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2wlnb4FV0RgN5K10JeSmqgrtDKpJ31KtFovMZkuhTm5uHuKCWmN1DK9OF6UXCsGIlSMbC63Id5w5pnhtFJS5AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:15.416956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ce516b0ba5587328883459030e7b81c1c691863a7281b9188a3abc90e85c291","sha256:d189a758be0755f2e1c2f1c7198866bf929b2fc4875153307baf231f67ac33af"],"state_sha256":"cce7f46d3998d041cf07c047b451674f8c983edef3a903e39caf2250e24ea773"}