Problem 835

Does there exist a $k>2$ such that the $k$ -sized subsets of $\{1,\ldots,2k\}$ 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 $A$ ?

Source: erdosproblems.com/835

Graph theory
Hypergraphs

Wiki page

Status

Open

No claim settles this problem.

Verifiable, the site's label for an open question whose positive answer a single finite coloring would witness; the label does not mean that such a coloring has been found. The site's page (last edited 22 January 2026) carries no proof claim. Two partial claim pages, Ma and Tang 2025 and AlphaProof 2026, record exclusions of particular $k$ ; neither settles the question, so the derived standing is open.

Problem 835

Status

Proof claims

Discussion