Ramsey Number

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Definition

Ramsey number R(m, n) is the solution to the party problems, which ask the minimum number of guests that must be invited so that at least m will know each other or at least n 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