Three-colouring arrangements of great circles

Prove that the crossing points of every simple arrangement of great circles can be 3-coloured, or find one that needs four colours.

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1	{
2	"domain": "computer-science",
3	"topics": [
4	"computational-geometry",
5	"graph-theory"
6	],
7	"type": "proof",
8	"also": [
9	"construction"
10	],
11	"cover": {
12	"motif": "graph",
13	"n": 6
14	},
15	"source": {
16	"key": "topp",
17	"name": "The Open Problems Project",
18	"url": "https://topp.openproblem.net/p44",
19	"id": "44",
20	"curator": "Erik D. Demaine, Joseph S. B. Mitchell and Joseph O'Rourke",
21	"poser": "Stan Wagon (zonohedra); Stefan Felsner, Ferran Hurtado, Marc Noy and Ileana Streinu (arrangements)",
22	"status": "open",
23	"as_of": "2026-10-20",
24	"catalog": "0521c19bbd38"
25	}
26	}