{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GSCAXF4XPH6KLS5T2XGY5JJMJT","short_pith_number":"pith:GSCAXF4X","schema_version":"1.0","canonical_sha256":"34840b979779fca5cbb3d5cd8ea52c4ce7a63a5d21eb7937f609a015a0bedd88","source":{"kind":"arxiv","id":"1707.09817","version":1},"attestation_state":"computed","paper":{"title":"Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Carl Feghali, Daniel Paulusma, Konrad K. Dabrowski, Marthe Bonamy, Matthew Johnson","submitted_at":"2017-07-31T12:32:54Z","abstract_excerpt":"We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets $A$ and~$B$, where $A$ is an independent set and $B$ induces a graph from some specified graph class ${\\cal G}$. We let ${\\cal G}$ be the class of $k$-degenerate graphs. This problem is known to be polynomial-time solvable if $k=0$ (bipartite graphs) and NP-complete if $k=1$ (near-bipartite graphs) even for graphs of maximum degree $4$. Yang and Yuan [DM, 2006] showed that the $k=1$ case is polynomial-time solvable for graphs of maximum degree $3$. This also follows"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.09817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-31T12:32:54Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"ce277bfa759389e078c791017e142d402e205604b6db3fbff27ca93156ddf3d8","abstract_canon_sha256":"1ac952c24795077e4df4ad75e6bf0dd502bf365553f60fe741bcf658d1e927b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:08.131421Z","signature_b64":"jsNeLc+h3XkRDbGvqxmPd/+MbJ7I4nwpPkjeUnanWQokyBjRGjQv2HtO5zdIoYFSmWjS/tdmq7kPdB9s8rL+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34840b979779fca5cbb3d5cd8ea52c4ce7a63a5d21eb7937f609a015a0bedd88","last_reissued_at":"2026-05-18T00:39:08.130705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:08.130705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Carl Feghali, Daniel Paulusma, Konrad K. Dabrowski, Marthe Bonamy, Matthew Johnson","submitted_at":"2017-07-31T12:32:54Z","abstract_excerpt":"We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets $A$ and~$B$, where $A$ is an independent set and $B$ induces a graph from some specified graph class ${\\cal G}$. We let ${\\cal G}$ be the class of $k$-degenerate graphs. This problem is known to be polynomial-time solvable if $k=0$ (bipartite graphs) and NP-complete if $k=1$ (near-bipartite graphs) even for graphs of maximum degree $4$. Yang and Yuan [DM, 2006] showed that the $k=1$ case is polynomial-time solvable for graphs of maximum degree $3$. This also follows"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09817","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.09817","created_at":"2026-05-18T00:39:08.130820+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.09817v1","created_at":"2026-05-18T00:39:08.130820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09817","created_at":"2026-05-18T00:39:08.130820+00:00"},{"alias_kind":"pith_short_12","alias_value":"GSCAXF4XPH6K","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GSCAXF4XPH6KLS5T","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GSCAXF4X","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT","json":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT.json","graph_json":"https://pith.science/api/pith-number/GSCAXF4XPH6KLS5T2XGY5JJMJT/graph.json","events_json":"https://pith.science/api/pith-number/GSCAXF4XPH6KLS5T2XGY5JJMJT/events.json","paper":"https://pith.science/paper/GSCAXF4X"},"agent_actions":{"view_html":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT","download_json":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT.json","view_paper":"https://pith.science/paper/GSCAXF4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.09817&json=true","fetch_graph":"https://pith.science/api/pith-number/GSCAXF4XPH6KLS5T2XGY5JJMJT/graph.json","fetch_events":"https://pith.science/api/pith-number/GSCAXF4XPH6KLS5T2XGY5JJMJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT/action/storage_attestation","attest_author":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT/action/author_attestation","sign_citation":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT/action/citation_signature","submit_replication":"https://pith.science/pith/GSCAXF4XPH6KLS5T2XGY5JJMJT/action/replication_record"}},"created_at":"2026-05-18T00:39:08.130820+00:00","updated_at":"2026-05-18T00:39:08.130820+00:00"}