

The Four Color Theorem And Algorithm - cjg
http://www.math.gatech.edu/~thomas/FC/fourcolor.html

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RiderOfGiraffes
This has been around for at least 10 years - the bottom of the web page says
"13 November 1995." As a PhD in graph theory I'm curious to know:

* why do you think this is interesting?

* what other 10 or 20 year old results might you be interested in? I have lots ...

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JoelSutherland
It is interesting because it is easy to understand the problem quickly --
we've all seen maps. Additionally, for graph theory, the solution is pretty
accessible.

I took just an introductory course in graph theory so I only got to see this
famous problem and a few others. I would think that this crowd would find a
list of other famous problems from your field quite interesting.

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RiderOfGiraffes
_the solution is pretty accessible._

I don't think that's true. I think you'll find the proof that discharging
gives you what you want is pretty impenetrable. And this is a review of a
survey paper that doesn't actually give the details.

I guess in this case I know too much about the topic to be able to assess
whether it will be interesting to a generic hacker. I think it's pretty
content-free. That's probably also the difference between me and a good
science writer. Anything I read about something I know seems to be complete
content-free fluff. I've tried, but I don't think I'll ever be able to write
anything for general consumption.

However, here are a couple of results and/or odd questions:

* Given a Turing Machine one can construct a graph such that 3-coloring the graph is equivalent to running the Turing machine.

 _> > Since 3-coloring doesn't have a "direction", that means you can
effectively run the TM backwards._

 _> >> That is a direct proof that 3-coloring is NP-complete._

* The set of reals is bigger than the set of integers

* One cannot decide from the axioms of set theory whether there is a set of reals that is bigger than the set of integers, but smaller than the set of reals.

* pi is very closely approximated by 355/113

* Define the sequence k(1)=0, k(2)=2, k(3)=3, k(n)=k(n-2)+k(n-3), and for n>1 ask: Does n divide k(n)? The answer is always "Yes" if n is prime, and almost always "No" if n is composite.

 __Challenge: find the first 5 cases where it gives the "wrong" answer.

Finally:

* What do you get if you photocopy a mirror?

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emmett
I found this post interesting. I'd subscribe to your blog if the posts were
about things like this.

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RiderOfGiraffes
Oh. Gosh. <fx: blush>

I might have to think about getting a blog, then ...

