Erdős Problem #1032
Erdős problem #1032 · erdosproblems.com/1032
Do arbitrarily large 4-chromatic edge-critical graphs exist with minimum degree bounded below by a positive constant times the number of vertices?
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Critical Graph Theory
- Posed by
- —
- Year posed
- 1973
- Years open
- 53y
- Solved
- 2026-05-07
- Model
- GPT-5.5 Pro, Codex
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
a new density-degree inequality gives δ(G) ≤ (3/10 + o(1))|V(G)|, improving 0.328; existence of a linear construction remains open
Verification
Lean-checked with expert screening.