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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13 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

835.lean

Retained formal statement5 of 13

Alternative statement of Erdős Problem 835 using the chromatic number of the Johnson graph. This is equivalent to asking whether there exists $k > 2$ such that the chromatic number of the Johnson graph $J(2k, k)$ is $k+1$ .

FormalConjectures/ErdosProblems/835.leanErdos835.erdos_835.variants.johnson1 lineExact file

1(∃ l, (SimpleGraph.johnson (2 * (l + 3)) (l + 3)).chromaticNumber = ↑(l + 3) + 1) ↔ sorry

OpenStatement only, no proof

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