Re:Tetrachromats: people who see colors invisible to most of...
by kragen on Monday November 18, 2019 @05:27PM
(#21568828)
It's correct, as you say, that if we can't build a map that ever requires a fifth colour, then it can't be that there exists a map which requires more than four.
It's just that the C₅-plus-thing requires four colors, even though it doesn't contain any K₄ induced subgraphs. So we could imagine that there might be some larger planar graph that requires 5 colors without containing K₅. As it turns out, there isn't, but that's the thing that's hard to prove.
Re:Tetrachromats: people who see colors invisible to most of...
by OJFord on Monday November 18, 2019 @07:56PM
(#21569817)
Hm, many thanks for the pointers. It's still not completely clear to me, but I have a much better idea and know the story of thing to search/read up on. Cheers.
It's just that the C₅-plus-thing requires four colors, even though it doesn't contain any K₄ induced subgraphs. So we could imagine that there might be some larger planar graph that requires 5 colors without containing K₅. As it turns out, there isn't, but that's the thing that's hard to prove.