{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WGBF5OMQQKUMPO5PTKN5BPDNBA","short_pith_number":"pith:WGBF5OMQ","schema_version":"1.0","canonical_sha256":"b1825eb99082a8c7bbaf9a9bd0bc6d080ae7d48a64d21b7eee8692c7ce2e4000","source":{"kind":"arxiv","id":"1804.09332","version":2},"attestation_state":"computed","paper":{"title":"Spanning trees with at most 4 leaves in $K_{1,5}-$free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dang Dinh Hanh, Pham Hoang Ha, Yuan Chen","submitted_at":"2018-04-25T03:15:44Z","abstract_excerpt":"In 2009, Kyaw proved that every $n$-vertex connected $K_{1,4}$-free graph $G$ with $\\sigma_4(G)\\geq n-1$ contains a spanning tree with at most $3$ leaves. In this paper, we prove an analogue of Kyaw's result for connected $K_{1,5}$-free graphs. We show that every $n$-vertex connected $K_{1,5}$-free graph $G$ with $\\sigma_5(G)\\geq n-1$ contains a spanning tree with at most $4$ leaves. Moreover, the degree sum condition `$\\sigma_5(G)\\geq n-1$' is best possible."},"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":"1804.09332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-25T03:15:44Z","cross_cats_sorted":[],"title_canon_sha256":"a62248a5effc84e40ff466a326fed95d5ccc215ff6dc832f861a5b6fd45329a8","abstract_canon_sha256":"5f8c2abb56825b9dc7be34e1e0c0673359b347b94834434b6bcbd7ee6d981417"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:49.450856Z","signature_b64":"jKf9HjV67cygumzqOrtAoLFVZiGKreNtkG5e+295ES7d9DaLhAdFcNw7EEmnIj0FmE5imEiLKdNfmZHAcs8qDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1825eb99082a8c7bbaf9a9bd0bc6d080ae7d48a64d21b7eee8692c7ce2e4000","last_reissued_at":"2026-05-18T00:02:49.450245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:49.450245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spanning trees with at most 4 leaves in $K_{1,5}-$free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dang Dinh Hanh, Pham Hoang Ha, Yuan Chen","submitted_at":"2018-04-25T03:15:44Z","abstract_excerpt":"In 2009, Kyaw proved that every $n$-vertex connected $K_{1,4}$-free graph $G$ with $\\sigma_4(G)\\geq n-1$ contains a spanning tree with at most $3$ leaves. In this paper, we prove an analogue of Kyaw's result for connected $K_{1,5}$-free graphs. We show that every $n$-vertex connected $K_{1,5}$-free graph $G$ with $\\sigma_5(G)\\geq n-1$ contains a spanning tree with at most $4$ leaves. Moreover, the degree sum condition `$\\sigma_5(G)\\geq n-1$' is best possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09332","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":""},"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":"1804.09332","created_at":"2026-05-18T00:02:49.450334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.09332v2","created_at":"2026-05-18T00:02:49.450334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09332","created_at":"2026-05-18T00:02:49.450334+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGBF5OMQQKUM","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGBF5OMQQKUMPO5P","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGBF5OMQ","created_at":"2026-05-18T12:32:59.047623+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/WGBF5OMQQKUMPO5PTKN5BPDNBA","json":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA.json","graph_json":"https://pith.science/api/pith-number/WGBF5OMQQKUMPO5PTKN5BPDNBA/graph.json","events_json":"https://pith.science/api/pith-number/WGBF5OMQQKUMPO5PTKN5BPDNBA/events.json","paper":"https://pith.science/paper/WGBF5OMQ"},"agent_actions":{"view_html":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA","download_json":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA.json","view_paper":"https://pith.science/paper/WGBF5OMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.09332&json=true","fetch_graph":"https://pith.science/api/pith-number/WGBF5OMQQKUMPO5PTKN5BPDNBA/graph.json","fetch_events":"https://pith.science/api/pith-number/WGBF5OMQQKUMPO5PTKN5BPDNBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA/action/storage_attestation","attest_author":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA/action/author_attestation","sign_citation":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA/action/citation_signature","submit_replication":"https://pith.science/pith/WGBF5OMQQKUMPO5PTKN5BPDNBA/action/replication_record"}},"created_at":"2026-05-18T00:02:49.450334+00:00","updated_at":"2026-05-18T00:02:49.450334+00:00"}