Let $k \geq 4$ and $g_{k} (n)$ denote the largest $m$ such that there is a graph on $n$ vertices with chromatic number $k$ and girth $> m$ (i.e. contains no cycle of length $\leq m$ ). Does $n \to \infty lim \frac{g _{k} ( n )}{lo g n}$ exist?Conversely, if $h^{(m)} (n)$ is the maximal chromatic number of a graph on $n$ vertices with girth $> m$ then does $n \to \infty lim \frac{lo g h ^{(m)} ( n )}{lo g n}$ exist, and what is its value?

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graph theory · open · possible · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

### 1) Fixed chromatic number $k$: the function (g_k(n))

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

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