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arXiv · 2610.02833

Resolving Erdős-Ulam Monochromatic Union-Closed Family Conjectures

Deep Bhattacharjee·Priyabrata Mandal·Ushashi Bhattacharya
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Abstract

We prove both Erdős-Ulam conjectures on monochromatic union-closed families. Every two-colouring of the subsets of a finite set contains a monochromatic union-closed family whose size grows faster than any fixed power of the size of the set, while suitable colourings admit no monochromatic union-closed family of exponential size. Both results hold for any number of colours and are verified in Lean.

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Deep Bhattacharjee, Priyabrata Mandal, Ushashi Bhattacharya. 2026-10-02. Resolving Erdős-Ulam Monochromatic Union-Closed Family Conjectures. https://arxiv.org/abs/2610.02833

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