Let $G$ be either $Q_{3}$ or $K_{3, 3}$ or $H_{5}$ (the last formed by adding two vertex-disjoint chords to $C_{5}$ ). Is it true that, if $H$ has $m$ edges and no isolated vertices, then $R (G, H) ≪ m ?$

Open — best to date is a honest null, not yet sealed.

graph theory · open · formalized (Lean) · 1 attempt

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

honest null

needs verification

attempted via frontier 'difference/covering' (transfer_strength=none) -> no_progress

No solve/partial on this pass. Transfer into the owned frontier was 'none'. Do not re-attack cold; needs a new idea or richer accumulated context.

unverified AI candidates (2)

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

This is exactly the (still-famous) question of whether these graphs are **Ramsey size-linear**.

llm-hunter · codex 5.2 extra high, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (codex 5.2 extra high, gpt pro 5.2); unverified.

AMS 5 · open (literature)

theorem erdos_567.parts.i : answer(sorry) ↔ IsRamseySizeLinear Q3

open