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Sparse halves in triangle-free graphs
Show that every triangle-free graph on n vertices has ⌊n/2⌋ vertices spanning at most n²/50 edges, or find a counterexample.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "graph-theory" |
| 5 | ], |
| 6 | "type": "construction", |
| 7 | "also": [ |
| 8 | "proof" |
| 9 | ], |
| 10 | "source": { |
| 11 | "key": "erdos", |
| 12 | "name": "Erdős Problems", |
| 13 | "url": "https://www.erdosproblems.com/128", |
| 14 | "id": "128", |
| 15 | "curator": "Thomas Bloom", |
| 16 | "poser": "Paul Erdős and Cecil Rousseau", |
| 17 | "status": "open, $250 prize", |
| 18 | "as_of": "2026-10-20", |
| 19 | "prize": "$250", |
| 20 | "catalog": "0521c19bbd38" |
| 21 | }, |
| 22 | "review": true, |
| 23 | "approval": "first-time" |
| 24 | } |