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Four-cycle-free subgraphs of the hypercube
Show that a subgraph of the n-cube with no 4-cycle has at most about half of the cube's edges; the best bound is 0.60318.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "graph-theory", | |
| 5 | + "combinatorics" | |
| 6 | + ], | |
| 7 | + "type": "proof", | |
| 8 | + "also": [ | |
| 9 | + "construction" | |
| 10 | + ], | |
| 11 | + "source": { | |
| 12 | + "key": "erdos", | |
| 13 | + "name": "Erdős Problems", | |
| 14 | + "url": "https://www.erdosproblems.com/86", | |
| 15 | + "id": "86", | |
| 16 | + "curator": "Thomas Bloom", | |
| 17 | + "poser": "Paul Erdős", | |
| 18 | + "status": "open, $100 prize", | |
| 19 | + "as_of": "2026-10-20", | |
| 20 | + "prize": "$100", | |
| 21 | + "catalog": "0521c19bbd38" | |
| 22 | + } | |
| 23 | +} | |