Problem Statement
Characterize those finite 3-uniform hypergraphs which appear in every 3-uniform hypergraph of chromatic number $>\aleph_0$.
Categories:
Set Theory Graph Theory Hypergraphs Chromatic Number
Progress
Similar problems were investigated by Erdős, Galvin, and Hajnal [EGH75]. Erdős claims that for graphs the problem is completely solved: a graph of chromatic number $\geq \aleph_1$ must contain all finite bipartite graphs but need not contain any fixed odd cycle.Source: erdosproblems.com/593 | Last verified: January 15, 2026