Erdős problem 835 · problems.science

Does there exist a $k>2$ such that the $k$ -sized subsets of {1,...,2k} can be coloured with $k+1$ colours such that for every $A\subset \{1,\ldots,2k\}$ with $\lvert A\rvert=k+1$ all $k+1$ colours appear among the $k$ -sized subsets of $A$ ?

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FormalConjectures/ErdosProblems/835.lean

Formal Conjectures

FormalConjectures/ErdosProblems/835.leanErdos835.chromaticNumber_johnson_2k_k_lower_bound1 lineExact file

1∀ {k : ℕ}, 3 ≤ k → k ≤ 8 → ↑k + 1 < (SimpleGraph.johnson (2 * k) k).chromaticNumber

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Formalization
Erdős AI contributions wiki · 26 Dec, 2025
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