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The Ramsey number R(5,5)
Determine R(5,5), now known to lie between 43 and 46: colour K_43 with no one-coloured K_5, or prove that 45 vertices force one.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "graph-theory", | |
| 5 | + "combinatorics" | |
| 6 | + ], | |
| 7 | + "type": "construction", | |
| 8 | + "also": [ | |
| 9 | + "proof" | |
| 10 | + ], | |
| 11 | + "cover": { | |
| 12 | + "motif": "graph", | |
| 13 | + "n": 8 | |
| 14 | + }, | |
| 15 | + "source": { | |
| 16 | + "key": "ramsey-survey", | |
| 17 | + "name": "Small Ramsey Numbers (Radziszowski, dynamic survey DS1)", | |
| 18 | + "url": "https://www.combinatorics.org/ds1", | |
| 19 | + "id": "R(5,5)", | |
| 20 | + "curator": "Stanisław Radziszowski", | |
| 21 | + "status": "open", | |
| 22 | + "as_of": "2026-10-20", | |
| 23 | + "catalog": "0521c19bbd38" | |
| 24 | + } | |
| 25 | +} | |