For a triangle-free graph $G$ let $h_{r} (G)$ be the smallest number of edges that need to be added to $G$ so that it has diameter $r$ (while preserving the property of being triangle-free).Is it true that there exists a constant $c > 0$ such that if $G$ is a connected graph on $n$ vertices then $h_{4} (G) < (1 - c) n$ ?

Worked, still open.

graph theory · open · 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

This is **open** (still not settled, as far as I can find).

llm-hunter · gpt pro 5.2 · unverified

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

open