Claims

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2011_01_01_borg: Borg (European J. Combin. 2011) proposes a weighted form of Chvátal's conjecture and proves it for weighted families with a dominant element, which with unit weights covers such families; refereed; partial.

2018_09_05_eifler_gleixner_pulaj: Eifler, Gleixner and Pulaj (ACM Trans. Math. Softw. 2022) verify Chvátal's conjecture for every downset on at most seven elements by exact integer programming with checked certificates; refereed; partial.

2022_01_11_frankl_kupavskii: Frankl and Kupavskii (Discrete Math. 2023) prove Chvátal's conjecture for intersecting subfamilies of covering number at most 2, through a disjointness matching between two down-sets; refereed; partial.

2026_09_16_chang_liu_liu: Chang, Liu and Liu's September 2026 preprint proves Chvátal's conjecture for subsets of a finite set through a sharp correlation inequality for increasing Boolean functions; not refereed, third-party Lean not built.

2026_09_20_keevash: Keevash's September 2026 preprint proves Kahn's flow conjecture in full generality, which implies Kleitman's and Chvátal's conjectures, sharpening the analysis of Chang, Liu and Liu; found with GPT-6 Astra, not refereed.

2026_09_23_ellis_filmus_friedgut: Ellis, Filmus and Friedgut's September 2026 note gives a two-page spectral proof of Chvátal's conjecture, a spectral proof of Kleitman's conjecture and a projection-packing strengthening; found with ChatGPT-6 Astra, unrefereed.

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