Erdős Problem #750

The problem

Let $f(m)$ be some function such that $f(m)\to \infty$ as $m\to \infty$. Does there exist a graph $G$ of infinite chromatic number such that every subgraph on $m$ vertices contains an independent set of size at least $\frac{m}{2}-f(m)$?

Statement quoted from erdosproblems.com/750, maintained by Thomas Bloom. Original source: [Er94b][Er95d]. Current status there: proved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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