<p>In addition to above, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS13" rel="nofollow">Ramsey theory apps by Rosta</a> (Electronic Journal of Combinatorics) also seems to have interesting notes on applications of Ramsey Numbers.  Also, I can perceive applications to Genetic Algorithms.  </p>

CC BY-SA 3.0
2011-12-26T18:38:34.523Z
2013-11-29T17:34:20.990Z
2013-11-29T17:34:20.990Z
Ahmed Masud
<ul>
<li><a href="http://www.cs.umd.edu/~gasarch/TOPICS/ramsey/ramsey.html" rel="nofollow">Applications of Ramsey theory to CS</a>, Gasarch</li>
</ul>

CC BY-SA 3.0
2013-02-11T03:11:39.527Z
Course in Ramsey Theory and Its "Applications" taught by Gasarch in Spring 2013: http://www.cs.umd.edu/~gasarch/858/S13/S13.html
Daniel Apon
CC BY-SA 3.0
2013-11-27T19:03:20.040Z
both urls 404 now =(
vzn
CC BY-SA 3.0
2013-11-27T20:32:02.460Z
@vzn http://www.cs.umd.edu/~gasarch/TOPICS/ramsey/ramsey.html
Sasho Nikolov
CC BY-SA 3.0
2013-11-29T17:40:47.803Z
re the class notes by apon link in comment. it is currently listed/broken also on [this UMD class pg](http://www.cs.umd.edu/class/) listing classes. maybe moved to [here](https://www.myedu.com/University-of-Maryland-College-Park/CMSC-858R-Advanced-Topics-In-Theory-Of-Computing-ramsey-Theory-And-Its-applications-/course/4734305/)?
vzn
CC BY-SA 3.0
2011-12-26T10:06:31.933Z
2013-11-29T17:39:04.280Z
2013-11-29T17:39:04.280Z
Sasho Nikolov
<p>The definition of Ramsey numbers is the following: </p>

<p>Let $R(a,b)$ be a positive number such that every graph of order at least $R(a,b)$ contains either a clique on $a$ vertices or a stable set on $b$ vertices.</p>

<p>I am working on some extension of Ramsey Numbers. While the study has some theoretical interest, it would be important to know the motivation of these numbers. More specifically I am wondering the (theoretical or practical) applications of Ramsey numbers. For instance, are there any solution methodology for a real life problem that uses Ramsey numbers? Or similarly, are there any proofs of some theorems based on Ramsey numbers?</p>

<reference-request><co.combinatorics><ramsey-theory>
Application of Ramsey Numbers
Arman
# Application of Ramsey Numbers

(Asked by: username_0 on 2011-12-26)

The definition of Ramsey numbers is the following:

Let $R(a,b)$ be a positive number such that every graph of order at least $R(a,b)$ contains either a clique on $a$ vertices or a stable set on $b$ vertices.

I am working on some extension of Ramsey Numbers. While the study has some theoretical interest, it would be important to know the motivation of these numbers. More specifically I am wondering the (theoretical or practical) applications of Ramsey numbers. For instance, are there any solution methodology for a real life problem that uses Ramsey numbers? Or similarly, are there any proofs of some theorems based on Ramsey numbers?

**Tags:** reference-request, co.combinatorics, ramsey-theory

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## 2 answers

### Answer by username_2 on 2011-12-26. Score: 22 | Accepted answer

* [Applications of Ramsey theory to CS](http://www.cs.umd.edu/~gasarch/TOPICS/ramsey/ramsey.html), Gasarch

> **Comments:**
> **username_3**: Course in Ramsey Theory and Its "Applications" taught by Gasarch in Spring 2013: http://www.cs.umd.edu/~gasarch/858/S13/S13.html  
> **username_4**: both urls 404 now =(  
> **username_2**: @vzn http://www.cs.umd.edu/~gasarch/TOPICS/ramsey/ramsey.html  
> **username_4**: re the class notes by apon link in comment. it is currently listed/broken also on [this UMD class pg](http://www.cs.umd.edu/class/) listing classes. maybe moved to [here](https://www.myedu.com/University-of-Maryland-College-Park/CMSC-858R-Advanced-Topics-In-Theory-Of-Computing-ramsey-Theory-And-Its-applications-/course/4734305/)?  

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### Answer by username_1 on 2011-12-26. Score: 3

In addition to above, [Ramsey theory apps by Rosta](http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS13) (Electronic Journal of Combinatorics) also seems to have interesting notes on applications of Ramsey Numbers. Also, I can perceive applications to Genetic Algorithms.


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