{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:EUGHGNU4L2LKMKYJC7QR3MPKPZ","short_pith_number":"pith:EUGHGNU4","schema_version":"1.0","canonical_sha256":"250c73369c5e96a62b0917e11db1ea7e7c2de7fc64b0b4c2194a5c1020aefdcd","source":{"kind":"arxiv","id":"1903.11268","version":1},"attestation_state":"computed","paper":{"title":"On graphs with no induced five-vertex path or paraglider","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Shenwei Huang, T. Karthick","submitted_at":"2019-03-27T07:10:24Z","abstract_excerpt":"Given two graphs $H_1$ and $H_2$, a graph is $(H_1,\\,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ or $H_2$. For a positive integer $t$, $P_t$ is the chordless path on $t$ vertices. A paraglider is the graph that consists of a chorless cycle $C_4$ plus a vertex adjacent to three vertices of the $C_4$. In this paper, we study the structure of ($P_5$, paraglider)-free graphs, and show that every such graph $G$ satisfies $\\chi(G)\\le \\lceil \\frac{3}{2}\\omega(G) \\rceil$, where $\\chi(G)$ and $\\omega(G)$ are the chromatic number and clique number of $G$, respectively. Our bound is"},"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":"1903.11268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T07:10:24Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"46857f6ea466049ad8e67c6241213240dd1a0b7b9ad0dcbe7869b7af825dc690","abstract_canon_sha256":"db82d80001ae140a643762a156cf7abad343db6a909b58ff004df1f653ff8b3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:03.713840Z","signature_b64":"hnQMrVBeckG8PpcecaIk+aKmhijj9rKfdYQ1Mrl6hiUedRsPuBycTQ0x+DhJjVgQ7z2VpA2+oCFst7YkKtmgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"250c73369c5e96a62b0917e11db1ea7e7c2de7fc64b0b4c2194a5c1020aefdcd","last_reissued_at":"2026-05-17T23:50:03.713333Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:03.713333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On graphs with no induced five-vertex path or paraglider","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Shenwei Huang, T. Karthick","submitted_at":"2019-03-27T07:10:24Z","abstract_excerpt":"Given two graphs $H_1$ and $H_2$, a graph is $(H_1,\\,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ or $H_2$. For a positive integer $t$, $P_t$ is the chordless path on $t$ vertices. A paraglider is the graph that consists of a chorless cycle $C_4$ plus a vertex adjacent to three vertices of the $C_4$. In this paper, we study the structure of ($P_5$, paraglider)-free graphs, and show that every such graph $G$ satisfies $\\chi(G)\\le \\lceil \\frac{3}{2}\\omega(G) \\rceil$, where $\\chi(G)$ and $\\omega(G)$ are the chromatic number and clique number of $G$, respectively. Our bound is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11268","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":"1903.11268","created_at":"2026-05-17T23:50:03.713433+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.11268v1","created_at":"2026-05-17T23:50:03.713433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11268","created_at":"2026-05-17T23:50:03.713433+00:00"},{"alias_kind":"pith_short_12","alias_value":"EUGHGNU4L2LK","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"EUGHGNU4L2LKMKYJ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"EUGHGNU4","created_at":"2026-05-18T12:33:15.570797+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/EUGHGNU4L2LKMKYJC7QR3MPKPZ","json":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ.json","graph_json":"https://pith.science/api/pith-number/EUGHGNU4L2LKMKYJC7QR3MPKPZ/graph.json","events_json":"https://pith.science/api/pith-number/EUGHGNU4L2LKMKYJC7QR3MPKPZ/events.json","paper":"https://pith.science/paper/EUGHGNU4"},"agent_actions":{"view_html":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ","download_json":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ.json","view_paper":"https://pith.science/paper/EUGHGNU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.11268&json=true","fetch_graph":"https://pith.science/api/pith-number/EUGHGNU4L2LKMKYJC7QR3MPKPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EUGHGNU4L2LKMKYJC7QR3MPKPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ/action/storage_attestation","attest_author":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ/action/author_attestation","sign_citation":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ/action/citation_signature","submit_replication":"https://pith.science/pith/EUGHGNU4L2LKMKYJC7QR3MPKPZ/action/replication_record"}},"created_at":"2026-05-17T23:50:03.713433+00:00","updated_at":"2026-05-17T23:50:03.713433+00:00"}