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· 2006 · arXiv 2303.17524

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math.CO 1

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2026 1

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CONDITIONAL 1

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Cover-free families on graphs

math.CO · 2026-05-12 · conditional · novelty 6.0

For any graph G, the minimum universe size for G-Sperner families equals the chromatic number of G, while G-cover-free families on paths and cycles satisfy log2(n) ≤ t ≤ 1.893 log2(n) + O(1).

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  • Cover-free families on graphs math.CO · 2026-05-12 · conditional · none · ref 29

    For any graph G, the minimum universe size for G-Sperner families equals the chromatic number of G, while G-cover-free families on paths and cycles satisfy log2(n) ≤ t ≤ 1.893 log2(n) + O(1).