Talk:Four color theorem

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"Three colors are adequate for simpler maps"

In the section regarding "real-world" maps, it says

"Three colors are adequate for simpler maps, but an additional fourth color is required for some maps, such as a map in which one region is surrounded by an odd number of other regions that touch each other in a cycle."

Surely it's actually very common for four colors to be required, such as when three countries/states are touching each other and the ocean. E.g. File:Map of Australia.png, or Central Europe. This seems even simpler than "one region is surrounded by an odd number of other regions that touch each other in a cycle," and common enough that the statement "three colors are adequate for simpler maps" seems quite out of place, since this kind of map is very simple and common indeed.

I'm going to remove the line, and the following line about 5-color-maps, since that was already mentioned earlier in the article, and, anyway, is proved a fortiori by the 4-color-theorem, so isn't actually relevant to the discussion on real-world maps. 50.255.135.49 (talk) 18:52, 14 September 2018 (UTC)

Hello, it's that dude formerly known as exxxz again. Somebody seems to agree with me

Somebody else has pointed out that any region with 3 or any higher odd number than 3 regions, surrounded by a ring of another colour, requires 4 colours, and that any region surrounded by 3 or any higher odd number of sectors also requires 4 colours. I pointed this out ages ago, along with some other fundamental 4 colour maps, for which I was completely rubbished. Have another look at my talk page post from ages ago, particularly the one in which I gave diagrams. I challenge anyone to post a map that I've not covered. Otherwise I'm right, aren't I Edmund Xathrusz (talk) 03:41, 13 December 2018 (UTC)

You're making a correct statement about something that's not in dispute, but I won't call it "right", since you're not even addressing the right question. It's well known that there are planar maps that require four colors; anybody can easily make one. The problem is to show that there are no maps that require more than four. I.e., "the set of maps that require five colors is empty".

This cannot be proved by the local analysis that you keep posting, because it's not true for some surfaces that are only locally planar. A projective plane requires six colors, and a torus requires seven. Joule36e5 (talk) 04:00, 13 December 2018 (UTC)

Reference consistency problem?

While reading the article, I noticed that while all of the references are in the references section, some of the inline harvard citations are done using traditional inline citation while some are done using the superscript method and the notes section used in most other Wikipedia articles. Examples of the notes method are found in paragraph 2 and 3 of the lead, while an example of regular Harvard citation (without superscript to notes section) is found prevalently in the Generalizations section.

I am wondering if this is allowed and considered consistent, or if we should make it more consistent, and if so which one should be adopted. From the last Good article nomination, it seems that referencing was the only major thing preventing it from becoming GA, and the article still seems well written except for this referencing issue. _{Integral Python} ^{click here to argue with me} 18:45, 8 March 2019 (UTC)

Contradiction in proof section?

The last paragraph in Four color theorem#Proof by computer: 'They responded that the rumors were due to a "misinterpretation of [Schmidt's] results" and obliged with a detailed article' - without further comment it looks like Schmidt was wrong. But then we learn that their book later " explained and corrected the error discovered by Schmidt [...]", so Schmidt was right? Related question: Why was it "a rumor" years after the master thesis was published? --mfb (talk) 07:22, 16 May 2019 (UTC)

Requested move 22 August 2020

Four color theorem → Four-color theorem – Punctuation Electricmaster (talk) 08:39, 22 August 2020 (UTC)

• Oppose on grounds given. Most of the scholarly, reliable sources don't punctuate this. See the references section, with titles like "The Four Color Theorem: History, Topological Foundations and Idea of Proof." There do appear to be a few sources that punctuate this, but we should follow the preponderance of the sources here. SnowFire (talk) 16:25, 22 August 2020 (UTC)
• Oppose per argument above, but Move to Four colour theorem for harmonize the grammar. 114.125.232.69 (talk) 16:48, 22 August 2020 (UTC)

That would involve switching from American English to English English. As Appel is American and Haken taught in America I think color is the most appropriate spelling to use.--Salix alba (talk): 16:57, 22 August 2020 (UTC)

Indeed, and since the article title has used the American spelling since its creation, MOS:RETAIN applies. Favonian (talk) 17:01, 22 August 2020 (UTC)

• Oppose - it's a theorem about four colors, not a theorem being four-color. --16:55, 22 August 2020 (UTC)
• Oppose because this article tells about a theorm about four colors, which IMO the correct title should be Four colour theorm for more NPOV title. 182.1.13.112 (talk) 16:59, 22 August 2020 (UTC)