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Let $\\mathcal{N}(R)$ be the nonseparating curve graph, $\\mathcal{C}(R)$ be the curve graph and $\\mathcal{HT}(R)$ be the Hatcher-Thurston graph of $R$. We prove that if $\\lambda : \\mathcal{N}(R) \\rightarrow\\mathcal{N}(R)$ is an edge-preserving map, then $\\lambda$ is induced by a homeomorphism of $R$. We prove that if $\\theta : \\mathcal{C}(R) \\rightarrow \\mathcal{C}(R)$ is an edge-preserving map, then $\\theta$ is induced by a homeomorphism of $R$. We prove that if $R$ is clo"},"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":"1708.05290","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-15T22:40:19Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d01ed1abad418046f17f1100c0eaed92159a030063637807ed1fbbfed7ead164","abstract_canon_sha256":"94b9b38f98eb9fb39ad19925a88394f157d428e699deef168e9a6425ea7ee3dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:33.469741Z","signature_b64":"hG9OFDAAPDYozbtE9tuhmyCNc0uBEEzZ2BIn6w8+vKCsdOOp7VjLfvaA+u2WrAvfsI+y/0GqoeT3XpeQj2C9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bc827ce592603ae48218f3204b53d7223ade272c580ea7b056a646d3998d33f","last_reissued_at":"2026-05-17T23:43:33.469324Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:33.469324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge Preserving Maps of the Nonseparating Curve Graphs, Curve Graphs and Rectangle Preserving Maps of the Hatcher-Thurston Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Elmas Irmak","submitted_at":"2017-08-15T22:40:19Z","abstract_excerpt":"Let $R$ be a compact, connected, orientable surface of genus $g$ with $n$ boundary components with $g \\geq 2$, $n \\geq 0$. Let $\\mathcal{N}(R)$ be the nonseparating curve graph, $\\mathcal{C}(R)$ be the curve graph and $\\mathcal{HT}(R)$ be the Hatcher-Thurston graph of $R$. We prove that if $\\lambda : \\mathcal{N}(R) \\rightarrow\\mathcal{N}(R)$ is an edge-preserving map, then $\\lambda$ is induced by a homeomorphism of $R$. We prove that if $\\theta : \\mathcal{C}(R) \\rightarrow \\mathcal{C}(R)$ is an edge-preserving map, then $\\theta$ is induced by a homeomorphism of $R$. 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