{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MKVWW7WTODH7P7IOEBZMCR2OMN","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":"188c21916e1f640f7f6e95a9f400c05d0b4cf378ad2427682bb08fbda5aef98e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-08T10:24:50Z","title_canon_sha256":"819f1e79e5f3c2a356eca5ce0f0c9b6b380da262b8cd8c963a00431523f3e8b3"},"schema_version":"1.0","source":{"id":"1702.02358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02358","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02358v1","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02358","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"MKVWW7WTODH7","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MKVWW7WTODH7P7IO","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MKVWW7WT","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:c32bda37d704f0ad93b60099cbcf58fef50e220dc905397f6fe2fde67bfc50b7","target":"graph","created_at":"2026-05-18T00:51:06Z","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":"A matching $M$ in a graph $G$ is $r$-degenerate if the subgraph of $G$ induced by the set of vertices incident with an edge in $M$ is $r$-degenerate. Goddard, Hedetniemi, Hedetniemi, and Laskar (Generalized subgraph-restricted matchings in graphs, Discrete Mathematics 293 (2005) 129-138) introduced the notion of acyclic matchings, which coincide with $1$-degenerate matchings. Solving a problem they posed, we describe an efficient algorithm to determine the maximum size of an $r$-degenerate matching in a given chordal graph. Furthermore, we study the $r$-chromatic index of a graph defined as th","authors_text":"Dieter Rautenbach, Julien Baste","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-08T10:24:50Z","title":"Degenerate Matchings and Edge Colorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02358","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":"sha256:7a6d442e6486e14ca7320e6d49076caf21ef8f8e7216d71f90bce86f2ad588d8","target":"record","created_at":"2026-05-18T00:51:06Z","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":"188c21916e1f640f7f6e95a9f400c05d0b4cf378ad2427682bb08fbda5aef98e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-08T10:24:50Z","title_canon_sha256":"819f1e79e5f3c2a356eca5ce0f0c9b6b380da262b8cd8c963a00431523f3e8b3"},"schema_version":"1.0","source":{"id":"1702.02358","kind":"arxiv","version":1}},"canonical_sha256":"62ab6b7ed370cff7fd0e2072c1474e635ec1ecd1a807f70c8058b8558ea76e44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62ab6b7ed370cff7fd0e2072c1474e635ec1ecd1a807f70c8058b8558ea76e44","first_computed_at":"2026-05-18T00:51:06.158478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:06.158478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"208GBRw8Gjuo1GnupiGBa9M5wVNsvlkR/DeDuMQReg99qR+4WHzDzCRiJVBd5koalmnlIb9KZCJhPYDC250PDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:06.158918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a6d442e6486e14ca7320e6d49076caf21ef8f8e7216d71f90bce86f2ad588d8","sha256:c32bda37d704f0ad93b60099cbcf58fef50e220dc905397f6fe2fde67bfc50b7"],"state_sha256":"4596f1444cb4c0eb6bbe55d66cda99bd73e21915a5459679517598c34779a9f2"}