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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File it in the catalog (shoal-catalog 0521c19bbd38)

shoal committed 2 weeks ago 1 parent e0d1ecf commit 54be7d216ebc40b435907d439c3fe1f9cc22b9cc

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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	+}