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We deduce this from recent work of Chudnovsky, Scott, Seymour, and Spirkl (2018). This proves the analog of the Erd\\H{o}s-Hajnal conjecture for vertex-minors."},"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":"1804.11008","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T00:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"838b337c3bea5ecb759522a21950f6fb1d5e04df68f2f535a1010101a277777d","abstract_canon_sha256":"c5d06d5fb78cc12c20ea7e816cb029202d92b53748b5a0ec4fb50578c1202efe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:07.737542Z","signature_b64":"KoZSyghMcZppUIpWgTbCOcM2nNuQbv+D0UBK1Uy3NUJeerQitN6oKgiW5ti72my+S2QOhzW9RD4xQ7WZaSigCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bd169c3821d97b800f18fa3c4117282431049ee42f382b2879a060384a872c2","last_reissued_at":"2026-05-18T00:04:07.736847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:07.736847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex-minors and the Erd\\H{o}s-Hajnal conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maria Chudnovsky, Sang-il Oum","submitted_at":"2018-04-30T00:35:06Z","abstract_excerpt":"We prove that for every graph $H$, there exists $\\varepsilon>0$ such that every $n$-vertex graph with no vertex-minors isomorphic to $H$ has a pair of disjoint sets $A$, $B$ of vertices such that $|A|, |B|\\ge \\varepsilon n$ and $A$ is complete or anticomplete to $B$. 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