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 $A$ ?

Sources

Browse retained paths and inspect the exact material available for this Problem.

13 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

835.lean

Retained formal statement8 of 13

Ma and Tang have proved that the chromatic number of $J(2k,k)$ is $>k+1$ for all $k>2$ not of the form $p-1$ for prime $p$ .

FormalConjectures/ErdosProblems/835.leanErdos835.johnson_chromaticNumber_composite1 lineExact file

1∀ (k : ℕ), 2 < k → (k + 1).Composite → ↑k + 1 < (SimpleGraph.johnson (2 * k) k).chromaticNumber

SolvedStatement only, no proof

Sources

Search problems.science