{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OTY27QIJ4GEW5VZ2BLESBDS6H7","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":"d4b1685e2e3080f5847af6a79a13235a671cde08c2324501d924e6f23be86c1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T12:53:13Z","title_canon_sha256":"4ad04f3d1f83997bd54806c4438b6244694e7fdf0a86a87740e03a6e683cf7f6"},"schema_version":"1.0","source":{"id":"1406.1671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1671","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1671v1","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1671","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"OTY27QIJ4GEW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OTY27QIJ4GEW5VZ2","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OTY27QIJ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:a98c16303d7bb92b44e25cfcb53dd1582b884ad836961ee5c16f274a54893be4","target":"graph","created_at":"2026-05-18T01:00:20Z","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":"We prove that any graph $G$ of minimum degree greater than $2k^2-1$ has a $(k+1)$-connected induced subgraph $H$ such that the number of vertices of $H$ that have neighbors outside of $H$ is at most $2k^2-1$. This generalizes a classical result of Mader, which states that a high minimum degree implies the existence of a highly connected subgraph. We give several variants of our result, and for each of these variants, we give asymptotics for the bounds. We also we compute optimal values for the case when $k=2$. Alon, Kleitman, Saks, Seymour, and Thomassen proved that in a graph of high chromati","authors_text":"Irena Penev, Nicolas Trotignon, St\\'ephan Thomass\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T12:53:13Z","title":"Isolating highly connected induced subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1671","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":"sha256:6cd16200354ac8b44b904222d404beefc3059b58a986f02b8f10e27370ea06a5","target":"record","created_at":"2026-05-18T01:00:20Z","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":"d4b1685e2e3080f5847af6a79a13235a671cde08c2324501d924e6f23be86c1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T12:53:13Z","title_canon_sha256":"4ad04f3d1f83997bd54806c4438b6244694e7fdf0a86a87740e03a6e683cf7f6"},"schema_version":"1.0","source":{"id":"1406.1671","kind":"arxiv","version":1}},"canonical_sha256":"74f1afc109e1896ed73a0ac9208e5e3fe4c93a59f5f7594b39c903b9ed8f18b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74f1afc109e1896ed73a0ac9208e5e3fe4c93a59f5f7594b39c903b9ed8f18b7","first_computed_at":"2026-05-18T01:00:20.525474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:20.525474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LLzVa7mWWz5jFGPmh9UkIfDBHsgCdefJ1uRCfb34RkMz3AHzyrwT0OYQpx4GB6up+ea3ybfQltBRCdZc7QuXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:20.526216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cd16200354ac8b44b904222d404beefc3059b58a986f02b8f10e27370ea06a5","sha256:a98c16303d7bb92b44e25cfcb53dd1582b884ad836961ee5c16f274a54893be4"],"state_sha256":"9ce73514d9efefd63c7c388569240a1e295a8b97ed1f79822b64408206528206"}