Ramsey Numbers: Links to Coursework Materials

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In summary, if you are looking for information on Ramsey numbers for a coursework, Google is a good place to start. The specific case of R(C4,K4) refers to the smallest number r where a red-blue coloring of a complete graph with r vertices contains either a red C4 or a blue K4.
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Naruto
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Could someone give me links to ramsey numbers related material, something that is siutable for a coursework. I would greatly appreciate if you could give me links that would help me find R(C4,K4)=?
 
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Yes, unfortunately I have spend several hours of googling before posting here with no success. I could only find reference to the ramsey theorem and to normal ramsey numbers R(m,n) m and n numbers, but I don't have a clue what to do when they are graphs as in my case R(C4,K4). I posted here in case someone have tackled the problem before
 
  • #4
What's [itex]C_4[/itex]?

Regardless, [itex]R(C_4,K_4)[/itex] is the smallest number [itex]r[/itex] so that a red-blue coloring of [itex]K_r[/itex] contains either a red [itex]C_4[/itex] or a blue [itex]K_4[/itex].
 

FAQ: Ramsey Numbers: Links to Coursework Materials

What are Ramsey Numbers?

Ramsey Numbers are a set of mathematical values that represent the minimum number of elements needed in a graph to guarantee a specific property. They are named after mathematician Frank P. Ramsey.

What is the significance of Ramsey Numbers?

Ramsey Numbers have applications in various fields such as computer science, telecommunications, and social sciences. They help in understanding the structure and complexity of networks and systems.

How are Ramsey Numbers calculated?

Ramsey Numbers are calculated using combinatorics and graph theory. There is no general formula for calculating them, and the values are usually found through exhaustive search methods or using advanced mathematical techniques.

What is the relationship between Ramsey Numbers and coursework materials?

Ramsey Numbers can be used as examples or case studies in coursework materials related to graph theory, combinatorics, and network analysis. They can also be used in practical assignments or projects to apply theoretical concepts.

What are some real-life examples that illustrate the concept of Ramsey Numbers?

Examples of real-life applications of Ramsey Numbers include scheduling problems, social networks, and data clustering. They can also be used in the design of efficient computer networks and routing algorithms.

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