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They further defined $\\mathcal{C}$ to be strongly Pollyanna if it is $k$-strongly Pollyanna for some integer $k$, meaning that $\\mathcal{C} \\cap \\mathcal{F}$ is polynomially $\\chi$-bounded for every $k$-good class $\\mathcal{F}$. They asked whether there are Pollyanna graph classes that are not strongly Pollyanna. 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They further defined $\\mathcal{C}$ to be strongly Pollyanna if it is $k$-strongly Pollyanna for some integer $k$, meaning that $\\mathcal{C} \\cap \\mathcal{F}$ is polynomially $\\chi$-bounded for every $k$-good class $\\mathcal{F}$. They asked whether there are Pollyanna graph classes that are not strongly Pollyanna. In this note we answer this question "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We construct a class C that is Pollyanna but, for every k ≥ 1, is not k-strongly Pollyanna; in particular C is not strongly Pollyanna.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Graph classes are not required to be hereditary, allowing the construction of a non-hereditary class C that separates the Pollyanna and strongly Pollyanna properties.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A non-hereditary graph class exists that is Pollyanna but not strongly Pollyanna.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A non-hereditary graph class exists that is Pollyanna but fails to be strongly Pollyanna for every k.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"be1069629c657579fa8a33693914e1876a759f121d11a05ef92a37b54e0e6f9d"},"source":{"id":"2605.14547","kind":"arxiv","version":1},"verdict":{"id":"288cd3e9-a257-468d-bed2-05a56aaed374","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:23:29.888026Z","strongest_claim":"We construct a class C that is Pollyanna but, for every k ≥ 1, is not k-strongly Pollyanna; in particular C is not strongly Pollyanna.","one_line_summary":"A non-hereditary graph class exists that is Pollyanna but not strongly Pollyanna.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Graph classes are not required to be hereditary, allowing the construction of a non-hereditary class C that separates the Pollyanna and strongly Pollyanna properties.","pith_extraction_headline":"A non-hereditary graph class exists that is Pollyanna but fails to be strongly Pollyanna for every k."},"references":{"count":7,"sample":[{"doi":"","year":2024,"title":"M. 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