{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4GXJQ36Z4HIL6LOPZNJ23ZD2L3","short_pith_number":"pith:4GXJQ36Z","schema_version":"1.0","canonical_sha256":"e1ae986fd9e1d0bf2dcfcb53ade47a5ed236673d23f37137be43a2d9b5ab24fb","source":{"kind":"arxiv","id":"2506.21286","version":2},"attestation_state":"computed","paper":{"title":"Infinitely many counterexamples to a conjecture of Lov\\'asz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aida Abiad, Christoph Spiegel, Frederik Garbe, Xavier Povill","submitted_at":"2025-06-26T14:06:41Z","abstract_excerpt":"Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in $r$-partite $r$-uniform hypergraphs, Lov\\'asz formulated a stronger conjecture. It states that one can always reduce the matching number by removing $r-1$ vertices. This conjecture was very recently disproven for $r=3$ by Clow, Haxell, and Mohar using the line graph of a $3$-regular graph of order $102$. Building on this, we describe a simple infinite family of counterexamples based on generalized Petersen graphs for the case $r=3$ and give specific counterexamples for $r=4$."},"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":"2506.21286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-26T14:06:41Z","cross_cats_sorted":[],"title_canon_sha256":"a3860b949e4649c665738f37b7c286d1545e4ca97ea2033ff9e5c7f50545f7c5","abstract_canon_sha256":"86350bceb778400d646af4329078ae8517510ba2ff14f584a3faa8746d59bda0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:56.251918Z","signature_b64":"+oF89B0jjCGTUtQjqWBAiSYFf3aMfbXQS1iDF9+RCqBLvk2kH13p9nXpOwoFLObPdll2iENYM9BkjRnbItgaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1ae986fd9e1d0bf2dcfcb53ade47a5ed236673d23f37137be43a2d9b5ab24fb","last_reissued_at":"2026-07-05T11:36:56.251346Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:56.251346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many counterexamples to a conjecture of Lov\\'asz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aida Abiad, Christoph Spiegel, Frederik Garbe, Xavier Povill","submitted_at":"2025-06-26T14:06:41Z","abstract_excerpt":"Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in $r$-partite $r$-uniform hypergraphs, Lov\\'asz formulated a stronger conjecture. It states that one can always reduce the matching number by removing $r-1$ vertices. This conjecture was very recently disproven for $r=3$ by Clow, Haxell, and Mohar using the line graph of a $3$-regular graph of order $102$. Building on this, we describe a simple infinite family of counterexamples based on generalized Petersen graphs for the case $r=3$ and give specific counterexamples for $r=4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21286","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.21286/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.21286","created_at":"2026-07-05T11:36:56.251408+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.21286v2","created_at":"2026-07-05T11:36:56.251408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21286","created_at":"2026-07-05T11:36:56.251408+00:00"},{"alias_kind":"pith_short_12","alias_value":"4GXJQ36Z4HIL","created_at":"2026-07-05T11:36:56.251408+00:00"},{"alias_kind":"pith_short_16","alias_value":"4GXJQ36Z4HIL6LOP","created_at":"2026-07-05T11:36:56.251408+00:00"},{"alias_kind":"pith_short_8","alias_value":"4GXJQ36Z","created_at":"2026-07-05T11:36:56.251408+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/4GXJQ36Z4HIL6LOPZNJ23ZD2L3","json":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3.json","graph_json":"https://pith.science/api/pith-number/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/graph.json","events_json":"https://pith.science/api/pith-number/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/events.json","paper":"https://pith.science/paper/4GXJQ36Z"},"agent_actions":{"view_html":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3","download_json":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3.json","view_paper":"https://pith.science/paper/4GXJQ36Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.21286&json=true","fetch_graph":"https://pith.science/api/pith-number/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/graph.json","fetch_events":"https://pith.science/api/pith-number/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/action/storage_attestation","attest_author":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/action/author_attestation","sign_citation":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/action/citation_signature","submit_replication":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/action/replication_record"}},"created_at":"2026-07-05T11:36:56.251408+00:00","updated_at":"2026-07-05T11:36:56.251408+00:00"}