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Scroll down a bit to https://en.m.wikipedia.org/wiki/Ramsey%27s_theorem#Ramsey_numbers https://en.m.wikipedia.org/wiki/Ramsey%27s_theorem#Ramsey_nu.... Ramsey n
by TheRealPomax 2y ago
Scroll down a bit to https://en.m.wikipedia.org/wiki/Ramsey%27s_theorem#Ramsey_numbers https://en.m.wikipedia.org/wiki/Ramsey%27s_theorem#Ramsey_nu.... Ramsey numbers arise from the original problem, and play a role in its proof, but they are not "the same thing" as Ramsey's Theorem.
- n4r9 2y agoSure, Ramsey's Theorem guarantees that Ramsey numbers exist. But at no point is it assumed that the graph is connected. The section you linked puts it quite simply: > The Ramsey number is the minimum number of vertices, v = R(m, n), such that all undirected simple graphs of order v, contain a clique of order m, or an independent set of order n. The graph is undirected and simple. But it need not be connected.