Erdős Problem #110 — Finite chromatic witnesses inside an aleph-one-chromatic graph

About 39 years old · traced to 1987

Given any function $f(n)→∞$ , is there a graph $G$ with chromatic number $ℵ_1$ such that, if $g_G(n)$ is the least number of vertices in an $n$ -chromatic subgraph of $G$ , then $f(n)/g_G(n)→0$ ?

References

Primary source

P. Erdős, Some problems on finite and infinite graphs, in Logic and Combinatorics, Contemporary Mathematics 65 (1987), 223–228.

Additional references

P. Erdős, Some problems on finite and infinite graphs, in Logic and Combinatorics, Contemporary Mathematics 65 (1987), 223–228.

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