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,n12345678910
1 1 1 1 1 1 1 1 1 1 1
212345678910
31369141823283640-43
4149182535-4149-6156-8473-11592-149
515142543-4958-8780-143101-216125-316143-442
6161835-4158-87102-165113-298127-495169-780179-1171
7172349-6180-143113-298205-540216-1031233-1713289-2826
8182856-84101-216127-495216-1031282-1870317-3583317-6090
9193673-115125-316169-780233-1713317-3583565-6588580-12677
1011040-4392-149143-442179-1171289-2826317-6090580-12677798-23556

Examples

References

[1] Weisstein, Eric W. Ramsey Number. From MathWorld--A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/RamseyNumber.html.

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