# 4 Color Theorem - What am I not seeing??

Let me say first that I am in no way a mathematician. Just slightly interested in mathematics. I think I may have found an exception to the 4 color theorem. I don't claim to be smarter than those who proved the theorem, and I'll assume I'm wrong. What am I missing here? (forgive my quickly drawn graph!)

(I created this account just to ask this question, so the website made me embed the image instead of just adding it straight to the question.)

I may be missing some fundamental rule in setting up my problem. But I think my map fits the desired intent of the "map" motif of the theorems original question.

• The green regions may be recolored red and purple. Commented Feb 20, 2021 at 23:40
• You can make the green pieces either red or purple. You don't need green. Commented Feb 20, 2021 at 23:40
• You've missed something indeed, and all those who wrote that monumental paper , and the computer which went through all those combinations ,are breathing a collective sigh of relief! But yes, the number of upvotes shows : it was not easy! Commented Feb 21, 2021 at 16:38
• In brief, the fact that you chose to use green for all three of those wedges does not mean they must all be the same color. The four-coloring does not make them the same color. Commented Feb 22, 2021 at 20:55
• Free software at Four Colour Problem Commented Feb 24, 2021 at 21:00

Here is your map colored with only four colours.

I've put numbers instead of colours (I left yours because whatever).

• You have used 5 colors instead of 4. Commented Feb 20, 2021 at 23:44
• @NitinUniyal If I had, I'm pretty sure I would have written a $5$ somewhere, which I did not.
– user239203
Commented Feb 20, 2021 at 23:45
• @NitinUniyal The colors are from the picture linked in the question, so ignore them if they're confusing you. The numbers represent the new 4-coloring Commented Feb 20, 2021 at 23:45
• You color code map is not bijective. Commented Feb 20, 2021 at 23:47
• oh...ok. I understood now. You superimposed your answer on the OP's attempt. Commented Feb 20, 2021 at 23:49

I don't think that you looked at it for long enough. By the way, you will not fault the theorem, it is proven.