# Four Corners and the Four Color Map Theorem

**URL:** <https://boards.straightdope.com/t/four-corners-and-the-four-color-map-theorem/5640>\
**Category:** Factual Questions\
**Created:** [December 29, 1999, 4:23pm UTC](https://boards.straightdope.com/t/four-corners-and-the-four-color-map-theorem/5640 "1999-12-29T16:23:00Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![system](https://global.discourse-cdn.com/straightdope/original/2X/e/e489c3b7d8fce19c4b355dd4fc3f88cc39c34b87.png) [@system](https://boards.straightdope.com/u/system)\
**Post date:** [December 29, 1999, 4:23pm UTC](https://boards.straightdope.com/t/four-corners-and-the-four-color-map-theorem/5640/1 "1999-12-29T16:23:00Z")

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On a website about my home state of Colorado, it lists Arizona as bordering it (at the CO/UT/AZ/NM Four Corners point).

But for purposes of map coloring, they aren’t considered bordering. Otherwise, the 4CMT would fail if you have 5 or more states meeting at a corner.

So, do Colorado and Arizona (or Utah and New Mexico) border each other or not?

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Everybody got to elevate from the norm - Rush

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**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\
**Post date:** [December 29, 1999, 5:08pm UTC](https://boards.straightdope.com/t/four-corners-and-the-four-color-map-theorem/5640/2 "1999-12-29T17:08:00Z")

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For purposes of map coloring and the four color theorem, two “countries” must share an edge not just a single point.

You are correct if “countries” sharing a single point were considered sharing a border, then there would be no upper limit on the number of colors necessary.

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Virtually yours,

DrMatrix