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.

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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	}