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In this note we prove that: (1) If $\\mu(G)\\geq n-4$, then $G$ is traceable unless $G=N_{n-3,3}$. (2) If $\\mu(\\overline{G})\\leq \\mu(\\overline{N_{n-3,3}})$ and $n\\geq 24$, then $G$ is traceable unless $G=N_{n-3,3}$. Our works are counterparts on claw-free graphs of previous theorems due to Lu et al., and Fiedler and Nikiforov, respectively."},"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":"1406.5404","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-20T14:34:28Z","cross_cats_sorted":[],"title_canon_sha256":"c59dcef4e35b1b118a59ef9382773efbc4af39a57de0db8e318d7df8e8e5d12c","abstract_canon_sha256":"50f3225e6decc8a2b5889829c9366682e5648fb231c9b399c08efc2950442434"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:58.366002Z","signature_b64":"7HymdmemeZQZSxdsqUPbZ5rjFBzL7rA/JgfBycmGzyHuQgchatRWlddXYgEJozEYe4f5kI9mDMVhdHSFUE9FBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03093e29644738a81b3a254dea8c44a37d29a2b394c543a5e58226fa7aa5a764","last_reissued_at":"2026-05-18T00:54:58.365584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:58.365584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral radius and traceability of connected claw-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning","submitted_at":"2014-06-20T14:34:28Z","abstract_excerpt":"Let $G$ be a connected claw-free graph on $n$ vertices and $\\overline{G}$ be its complement graph. Let $\\mu(G)$ be the spectral radius of $G$. Denote by $N_{n-3,3}$ the graph consisting of $K_{n-3}$ and three disjoint pendent edges. In this note we prove that: (1) If $\\mu(G)\\geq n-4$, then $G$ is traceable unless $G=N_{n-3,3}$. (2) If $\\mu(\\overline{G})\\leq \\mu(\\overline{N_{n-3,3}})$ and $n\\geq 24$, then $G$ is traceable unless $G=N_{n-3,3}$. Our works are counterparts on claw-free graphs of previous theorems due to Lu et al., and Fiedler and Nikiforov, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5404","kind":"arxiv","version":4},"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":"1406.5404","created_at":"2026-05-18T00:54:58.365650+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5404v4","created_at":"2026-05-18T00:54:58.365650+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5404","created_at":"2026-05-18T00:54:58.365650+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMET4KLEI44K","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMET4KLEI44KQGZ2","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMET4KLE","created_at":"2026-05-18T12:28:19.803747+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/AMET4KLEI44KQGZ2EVG6VDCEUN","json":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN.json","graph_json":"https://pith.science/api/pith-number/AMET4KLEI44KQGZ2EVG6VDCEUN/graph.json","events_json":"https://pith.science/api/pith-number/AMET4KLEI44KQGZ2EVG6VDCEUN/events.json","paper":"https://pith.science/paper/AMET4KLE"},"agent_actions":{"view_html":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN","download_json":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN.json","view_paper":"https://pith.science/paper/AMET4KLE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5404&json=true","fetch_graph":"https://pith.science/api/pith-number/AMET4KLEI44KQGZ2EVG6VDCEUN/graph.json","fetch_events":"https://pith.science/api/pith-number/AMET4KLEI44KQGZ2EVG6VDCEUN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/action/storage_attestation","attest_author":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/action/author_attestation","sign_citation":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/action/citation_signature","submit_replication":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/action/replication_record"}},"created_at":"2026-05-18T00:54:58.365650+00:00","updated_at":"2026-05-18T00:54:58.365650+00:00"}