Problem 62

Erdős Problem #62: declared status 'open'. Formalized: no. If $G_1,G_2$ are two graphs with chromatic number $\aleph_1$ then must there exist a graph $G$ whose chromatic number is $4$ (or even $\aleph_0$) which is a subgraph of both $G_1$ and $G_2$? Prize: no. Tags: graph theory.