Ramsey Number
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Definition
Ramsey number 
is the solution to the party problems, which ask the minimum number of guests that must be invited so that at least 
will know each other or at least 
will not know each other.
A Summary of Known Ramsey Numbers
| m,n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 3 | 1 | 3 | 6 | 9 | 14 | 18 | 23 | 28 | 36 | 40-43 |
| 4 | 1 | 4 | 9 | 18 | 25 | 35-41 | 49-61 | 56-84 | 73-115 | 92-149 |
| 5 | 1 | 5 | 14 | 25 | 43-49 | 58-87 | 80-143 | 101-216 | 125-316 | 143-442 |
| 6 | 1 | 6 | 18 | 35-41 | 58-87 | 102-165 | 113-298 | 127-495 | 169-780 | 179-1171 |
| 7 | 1 | 7 | 23 | 49-61 | 80-143 | 113-298 | 205-540 | 216-1031 | 233-1713 | 289-2826 |
| 8 | 1 | 8 | 28 | 56-84 | 101-216 | 127-495 | 216-1031 | 282-1870 | 317-3583 | 317-6090 |
| 9 | 1 | 9 | 36 | 73-115 | 125-316 | 169-780 | 233-1713 | 317-3583 | 565-6588 | 580-12677 |
| 10 | 1 | 10 | 40-43 | 92-149 | 143-442 | 179-1171 | 289-2826 | 317-6090 | 580-12677 | 798-23556 |
Examples
References
[1] Weisstein, Eric W. Ramsey Number. From MathWorld--A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/RamseyNumber.html.
