{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZFZFESBYMNXFED5F45OCQPXR5H","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":"ce14d66d83055628e410aee9f00b384d49dbee3c6801dd389d1bed31fee5d0ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-06T08:17:37Z","title_canon_sha256":"a2bdbcf52bd5615b00c1e00e99ac2f4da5845b7bbb3eef06952274fbaf6a434e"},"schema_version":"1.0","source":{"id":"1807.02308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02308","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02308v1","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02308","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZFZFESBYMNXF","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZFZFESBYMNXFED5F","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZFZFESBY","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:06af14ba79e91d9896399d75658e0525eb07788e8180878723cd1137ff908577","target":"graph","created_at":"2026-05-18T00:11:22Z","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 2007 Matamala proved that if $G$ is a simple graph with maximum degree $\\Delta\\geq 3$ not containing $K_{\\Delta +1}$ as a subgraph and $s, t$ are positive integers such that $s+t \\geq \\Delta$, then the vertex set of $G$ admits a partition $(S,T)$ such that $G[S]$ is a maximum order $(s-1)$-degenerate subgraph of $G$ and $G[T]$ is a $(t-1)$-degenerate subgraph of $G$. This result extended earlier results obtained by Borodin, by Bollob\\'as and Manvel, by Catlin, by Gerencs\\'{e}r and by Catlin and Lai. In this paper we prove a hypergraph version of this result and extend it to variable degener","authors_text":"Michael Stiebitz, Thomas Schweser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-06T08:17:37Z","title":"Vertex partition of hypergraphs and maximum degenerate subhypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02308","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":"sha256:4b6ce6be49bf941b8f9868cd265831d3311c30315b201109b41f2f869401763f","target":"record","created_at":"2026-05-18T00:11:22Z","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":"ce14d66d83055628e410aee9f00b384d49dbee3c6801dd389d1bed31fee5d0ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-06T08:17:37Z","title_canon_sha256":"a2bdbcf52bd5615b00c1e00e99ac2f4da5845b7bbb3eef06952274fbaf6a434e"},"schema_version":"1.0","source":{"id":"1807.02308","kind":"arxiv","version":1}},"canonical_sha256":"c972524838636e520fa5e75c283ef1e9d5d7249f0870ec8db4dbe144ca06f9ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c972524838636e520fa5e75c283ef1e9d5d7249f0870ec8db4dbe144ca06f9ab","first_computed_at":"2026-05-18T00:11:22.434521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:22.434521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D0X4DvTPiprLiIPx+FycYpqlmb667tQAX0MjlyBhF9uMXe4MDrVkhfKyC7A1aIc8p5ceGTO1BT8Ol95FlDuBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:22.435242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b6ce6be49bf941b8f9868cd265831d3311c30315b201109b41f2f869401763f","sha256:06af14ba79e91d9896399d75658e0525eb07788e8180878723cd1137ff908577"],"state_sha256":"0953acff1f0b462e0f83e1ccf9a98a776e3641f55cde497407e6497954cc3efc"}